Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#532 ◁ G | |
2060 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)(18,19,21,23)(20,24,25,22)(26,27)(28,33)(29,35)(30,37)(31,36)(32,38)(34,42)(39,47)(40,52)(41,49)(43,51)(44,48)(45,50)(46,54)(53,57)(55,56);(18,20)(19,22)(21,25)(23,24)(26,28,32,41)(27,33,38,49)(29,39,43,55)(30,44,31,40)(34,46,50,57)(35,47,51,56)(36,52,37,48)(42,54,45,53);(26,29)(27,34)(28,39)(30,42)(31,45)(32,43)(33,46)(35,36)(37,51)(38,50)(40,53)(41,55)(44,54)(47,52)(48,56)(49,57);(20,25)(22,24)(26,29)(27,35)(28,39)(30,45)(31,42)(32,43)(33,47)(34,36)(37,50)(38,51)(40,54)(41,55)(44,53)(46,52)(48,57)(49,56);(26,30,32,31)(27,36,38,37)(28,40,41,44)(29,42,43,45)(33,48,49,52)(34,35,50,51)(39,53,55,54)(46,56,57,47)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54204);