Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#12660 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #117 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | #432 |
| prime radical | C23×C17 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#97 ◁ G | |
330 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)(18,19,20,21)(22,23)(24,32)(25,37)(26,31)(27,29)(28,34)(30,38)(33,41)(35,42)(36,45)(39,51)(40,43)(44,47)(46,49)(48,53)(50,52);(19,21)(22,24,25,35,26,36,39,50,27,34,38,49,40,33,47,48)(23,28,30,42,31,41,44,52,29,32,37,46,43,45,51,53);(23,29)(24,33,34,36)(25,38)(28,41,32,45)(31,43)(35,50,49,48)(39,47)(42,53,46,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5648);