Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61224 |
| 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 | |
2020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(26,27,31,37)(28,35,41,33)(29,42,45,53)(30,38,32,36)(34,47,51,44)(39,54,43,57)(40,49,46,52)(48,56,50,55);(18,20)(19,22)(21,25)(23,24)(26,28,31,41)(27,33,37,35)(29,43,45,39)(30,46,32,40)(34,50,51,48)(36,52,38,49)(42,54,53,57)(44,55,47,56);(26,29,31,45)(27,34,37,51)(28,39,41,43)(30,44,32,47)(33,48,35,50)(36,42,38,53)(40,55,46,56)(49,54,52,57);(20,25)(22,24)(26,28)(27,35)(29,39)(30,46)(31,41)(32,40)(33,37)(34,50)(36,49)(38,52)(42,54)(43,45)(44,56)(47,55)(48,51)(53,57);(26,30,31,32)(27,36,37,38)(28,40,41,46)(29,44,45,47)(33,49,35,52)(34,42,51,53)(39,55,43,56)(48,54,50,57)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54212);