Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#20569 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C2 | C22×C4×C8×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle, prime radical | C23×C17 | C23×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23)(24,27)(25,28)(26,29)(30,31,33,36,34,32,35,37);(18,19,20,21)(22,24,27,23)(25,28,26,29);(22,25,27,26)(23,28,24,29)(30,32,33,37,34,31,35,36);(22,26,27,25)(23,28,24,29)2312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13557);