Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#3414 ⋊ C2 |
| Sylow | C79 ⋊ #13312 |
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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:
(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)(81,89)(82,95)(84,102)(85,110)(86,103)(87,104)(88,111)(90,115)(91,116)(92,100)(93,117)(94,122)(96,125)(97,101)(98,126)(99,127)(105,132)(106,134)(107,139)(108,137)(109,138)(112,141)(113,131)(114,121)(118,143)(119,142)(120,135)(123,133)(124,130)(128,140)(129,136);(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)(81,88)(83,101)(84,106)(85,97)(86,98)(87,99)(89,114)(90,118)(91,112)(92,121)(93,113)(94,105)(95,103)(96,108)(100,131)(102,136)(104,126)(107,129)(109,128)(110,127)(111,116)(115,122)(117,141)(119,123)(120,130)(124,132)(125,138)(133,135)(134,137)(139,140)(142,143);(80,81)(82,94)(83,100)(84,105)(85,92)(86,91)(87,93)(88,96)(89,103)(90,108)(95,124)(97,130)(98,118)(99,123)(101,133)(102,135)(104,116)(106,121)(107,120)(109,119)(110,117)(111,140)(112,128)(113,129)(114,125)(115,138)(122,126)(127,143)(131,134)(132,137)(136,141)(139,142)Polycyclic presentation:
2^8,79|d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,c^b=cf,d^b=dg,f^b=fh,g^b=gh,e^c=eh,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, 88312);