Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#7460 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | D16 |
| commutator | C16 | C2×C8×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| socle, prime radical | C22×C17 | #366 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ C4×C16×C17 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 2 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(27,32)(28,33)(29,37)(30,40)(34,49)(35,52)(36,45)(38,54)(39,48)(41,53)(42,43)(44,50)(46,47)(51,57)(55,56);(26,27,33,43,29,34,46,52,40,50,54,57,53,55,39,45,31,36,48,56,41,51,38,44,30,35,47,49,37,42,28,32)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 448);