Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#10956 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #386 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
918 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)(22,23)(24,33)(25,37,39,46)(26,40)(27,31)(28,32)(29,35)(30,38,47,42)(34,49,52,43)(36,44)(41,45)(48,51,53,50);(18,19,20,21)(22,24)(23,29)(25,34)(26,41)(27,35)(28,36)(30,43)(31,44)(32,45)(33,40)(37,48)(38,51)(39,52)(42,50)(46,53)(47,49);(22,25,27,42,28,39,26,38)(23,30,31,46,32,47,40,37)(24,34,35,50,36,52,41,51)(29,43,44,53,45,49,33,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3944);