Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10803 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | C4×C22⋊C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23)(24,28)(25,35,36,29)(26,31)(27,30)(32,44,45,39)(33,41)(34,40)(37,48,49,42)(38,43)(46,52,53,50)(47,51);(18,19,21,20)(22,24,26,33,27,34,38,47)(23,28,31,41,30,40,43,51)(25,32,37,46,36,45,49,53)(29,39,42,50,35,44,48,52);(18,20,21,19)(22,25)(23,29)(24,32)(26,37)(27,36)(28,39)(30,35)(31,42)(33,46)(34,45)(38,49)(40,44)(41,50)(43,48)(47,53)(51,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3791);