Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#12654 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C17 | C23 |
| commutator | C22 | C2×C4×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle, prime radical | C23×C17 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C17 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23,25,24)(26,27)(28,32)(29,34)(30,35)(31,33)(36,43)(37,44)(38,42)(39,47)(40,45)(41,46)(48,54)(49,52)(50,53)(51,55)(56,57);(19,21)(26,28,29,36,30,37,39,48,31,38,40,49,41,50,51,56)(27,32,34,43,35,44,47,54,33,42,45,52,46,53,55,57);(22,24,25,23)(27,33)(32,42)(34,45)(35,46)(43,52)(44,53)(47,55)(54,57)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5642);