Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #563×C157 ⋊ C2 |
| Sylow | C157 ⋊ #2203 |
216 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 189 |
| transitive degree | μt(G) = 5024 |
A minimal faithful permutation representation — 3 generators on 189 points:
(2,8)(5,21)(7,23)(9,28)(10,11)(12,29)(14,20)(16,26)(18,22)(24,25)(27,30)(31,32)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,144,146,148,150,152,154,156,158,160,162,164,166,168,170,172,174,176,178,180,182,184,186,188,189,187,185,183,181,179,177,175,173,171,169,167,165,163,161,159,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,3,6,15)(2,7,11,25)(4,17,19,13)(5,20,21,14)(8,23,10,24)(9,27,16,12)(18,31,22,32)(26,29,28,30);(1,2)(3,12)(4,16)(5,8)(6,11)(7,13)(9,19)(10,21)(14,29)(15,27)(17,25)(18,26)(20,30)(22,28)(23,31)(24,32)(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)(158,159)(160,161)(162,163)(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)(178,179)(180,181)(182,183)(184,185)(186,187)(188,189)Polycyclic presentation:
2^7,157|b^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^156,d^b=dg,e^b=efg,d^c=df,e^c=eg,e^d=eg1499 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 6531);