Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61198 |
| 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×#525 ◁ G | |
2046 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)(28,38)(29,42)(30,35)(31,37)(32,36)(33,41)(34,43)(39,53)(40,49)(44,50)(45,48)(46,51)(47,54)(52,56)(55,57);(18,20)(19,22)(21,25)(23,24)(26,28,31,41)(27,33,37,38)(29,39,44,55)(30,45,32,40)(34,47,51,52)(35,49,36,48)(42,57,50,53)(43,56,46,54);(26,29)(27,34)(28,39)(30,43)(31,44)(32,46)(33,47)(35,50)(36,42)(37,51)(38,52)(40,54)(41,55)(45,56)(48,57)(49,53);(20,25)(22,24)(26,30,31,32)(27,35,37,36)(28,40,41,45)(29,43,44,46)(33,48,38,49)(34,50,51,42)(39,54,55,56)(47,57,52,53);(26,30,31,32)(27,36,37,35)(28,40,41,45)(29,43,44,46)(33,49,38,48)(34,42,51,50)(39,54,55,56)(47,53,52,57)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54186);