Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#1738 ⋊ C2 |
| Sylow | C79 ⋊ #10767 |
1148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 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)(85,99)(86,100)(87,101)(89,104)(90,97)(91,105)(92,106)(94,108)(95,110)(96,109)(102,111)(103,107);(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)(80,82,85,94,86,96,84,95)(81,87,89,103,90,102,91,92)(83,93,99,108,100,109,98,110)(88,101,104,107,97,111,105,106);(80,81,84,91,86,90,85,89)(82,92,95,102,96,103,94,87)(83,97,99,105,100,88,98,104)(93,107,108,111,109,106,110,101)Polycyclic presentation:
2^8,79|a^2=f,b^2=g,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,d^b=dh,f^c=fh,i^c=i^781774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 75012);