Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#2141 ⋊ C2 |
| Sylow | C79 ⋊ #12742 |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 points:
(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)(80,83)(81,88)(82,93)(84,98)(85,100)(86,99)(87,108)(89,111)(90,97)(91,112)(92,117)(94,120)(95,122)(96,121)(101,135)(102,130)(103,131)(104,133)(105,132)(106,128)(107,134)(109,126)(110,137)(113,138)(114,127)(115,139)(116,129)(118,119)(123,141)(124,142)(125,140)(136,143);(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)(80,82,86,96)(81,87,90,109)(83,93,99,121)(84,102,105,136)(85,107,103,95)(88,108,97,126)(89,113,114,125)(91,115,106,110)(92,116,118,101)(94,123,124,104)(98,130,132,143)(100,134,131,122)(111,138,127,140)(112,139,128,137)(117,129,119,135)(120,141,142,133);(80,81)(82,92)(83,97,99,88)(84,101)(85,106)(86,90)(87,94)(89,104)(91,103)(93,119,121,117)(95,125)(96,118)(98,129,132,135)(100,112,131,128)(102,115)(105,116)(107,113)(108,120,126,142)(109,124)(110,136)(111,133,127,141)(114,123)(122,138,134,140)(130,137,143,139)Polycyclic presentation:
2^8,79|a^2=f,b^2=h,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,d^b=dg,g^b=gh,f^c=fh,i^c=i^781288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85257);