Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#12641 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | D8 |
| commutator | C8 | C2×C42×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C4×D8 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
438 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)(22,23,26,33,29,34,28,43)(24,35,37,45,40,51,39,53)(25,31,41,48,42,49,27,32)(30,44,46,52,47,38,50,36);(19,21)(22,24,27,38,28,39,42,52,29,40,41,44,26,37,25,36)(23,30,31,45,33,46,48,51,34,47,49,53,43,50,32,35);(22,25,26,41,29,42,28,27)(23,31,33,48,34,49,43,32)(24,36,37,44,40,52,39,38)(30,45,46,51,47,53,50,35)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5629);