Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#346×C79 ⋊ C2 |
| Sylow | C79 ⋊ #11588 |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 119 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)(89,95)(90,99)(96,108)(97,109)(100,102)(101,113)(111,118)(114,115);(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)(81,84)(82,87)(85,86)(88,90)(89,94)(91,102)(92,99)(93,101)(95,98)(96,110)(97,107)(100,103)(104,115)(105,113)(106,108)(109,112)(111,119)(114,116)(117,118);(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)(82,84)(83,86)(85,87)(88,89,91,96,93,97,104,111,92,95,103,108,105,109,116,118)(90,98,100,110,101,112,114,119,99,94,102,106,113,107,115,117)Polycyclic presentation:
2^8,79|a^2=e,d^2=fh,e^2=g,g^2=h,b^a=bd,c^a=ch,d^a=df,i^a=i^78,c^b=ch,d^b=dfh,e^b=eh,i^b=i^783184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79296);