Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60557 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#117 ◁ G | |
2038 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,33)(29,41)(30,35)(31,44)(32,36)(34,42)(37,51)(38,47)(39,48)(40,54)(43,49)(45,50)(46,53)(52,57)(55,56);(19,22)(23,25)(26,28)(27,33)(29,37)(30,39)(31,40)(32,38)(34,46)(35,48)(36,47)(41,51)(42,53)(43,52)(44,54)(45,55)(49,57)(50,56);(26,29)(27,34)(28,37)(30,42)(31,45)(32,43)(33,46)(35,49)(36,50)(38,52)(39,53)(40,55)(41,44)(47,56)(48,57)(51,54);(18,20,21,24)(19,23,22,25)(28,38)(33,47)(37,52)(39,40)(46,56)(48,54)(51,57)(53,55);(26,30,32,31)(27,35,36,44)(28,39,38,40)(29,42,43,45)(33,48,47,54)(34,49,50,41)(37,53,52,55)(46,57,56,51)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53545);