Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #2222 |
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 221 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 3 generators on 221 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,144,146,148,150,152,154,156,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(158,161)(159,167)(160,174)(162,180)(163,186)(164,181)(165,182)(166,188)(168,192)(169,196)(170,179)(171,193)(172,197)(173,202)(175,204)(176,208)(177,205)(178,206)(183,210)(184,213)(185,212)(187,214)(189,217)(190,209)(191,216)(194,218)(195,211)(198,220)(199,203)(200,219)(201,221)(207,215);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,160,173,201,164,177,185,187,165,178,184,207,163,176,162,175)(159,166,183,199,170,190,195,200,171,191,194,198,169,189,168,172)(161,174,202,221,181,205,212,214,182,206,213,215,186,208,180,204)(167,188,210,203,179,209,211,219,193,216,218,220,196,217,192,197);(158,159,165,171)(160,172,178,200)(161,179,182,196)(162,183,185,194)(163,170,164,169)(166,187,191,175)(167,186,193,181)(168,184,195,173)(174,203,206,220)(176,199,177,198)(180,211,212,192)(188,215,216,221)(189,207,190,201)(197,208,219,205)(202,210,213,218)(204,209,214,217)Polycyclic presentation:
2^7,157|a^2=g,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^b=h^156,e^c=eg1274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 6633);