Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#2221 ⋊ C2 |
| Sylow | C79 ⋊ #13670 |
278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,82,87,96)(81,89,92,115)(83,94,102,124)(84,103,86,93)(85,95,106,125)(88,108,110,136)(90,114,107,112)(91,113,118,139)(97,123,129,141)(98,122,130,143)(99,120,104,133)(100,131,101,119)(105,126,134,138)(109,135,116,111)(117,140,132,137)(121,127,142,128);(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)(82,89)(83,98)(84,90)(85,105)(86,107)(87,92)(88,97)(91,99)(93,112)(94,122)(95,126)(96,115)(100,117)(101,132)(102,130)(103,114)(104,118)(106,134)(108,123)(109,127)(110,129)(111,121)(113,120)(116,128)(119,137)(124,143)(125,138)(131,140)(133,139)(135,142)(136,141);(81,88)(82,93)(83,97)(84,86)(85,99)(89,111)(90,116)(91,117)(92,110)(94,121)(95,125)(96,103)(98,105)(100,128)(101,127)(102,129)(104,106)(107,109)(108,112)(113,122)(114,136)(115,135)(118,132)(119,123)(124,142)(126,137)(130,134)(131,141)(138,140)(139,143)Polycyclic presentation:
2^8,79|c^2=h,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,d^b=df,f^b=fg,g^b=gh,i^b=i^78,e^c=eh1051 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90257);