Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #9178 |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 111 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)(80,83,85,84)(81,87,89,88)(82,91,93,92)(86,94,95,90)(96,98)(97,102)(99,107)(100,105)(101,109)(103,110)(104,111)(106,108);(80,82)(81,86)(83,91)(84,92)(85,93)(87,94)(88,90)(89,95)(96,98)(97,101,103,111)(99,107)(100,105)(102,109,110,104)(106,108);(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)(80,81,84,88,85,89,83,87)(82,90,91,86,93,94,92,95)(96,97)(98,101,105,111)(99,104)(100,103)(102,106,110,107)(108,109)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=gh,d^2=gh,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^78,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=eg,f^c=fg1993 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 65496);