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×#61338 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1732 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)(19,22)(23,24)(26,27,31,35)(28,37,39,33)(29,41,43,51)(30,36,32,45)(34,46,50,42)(38,53,54,57)(40,49,44,48)(47,56,52,55);(18,19,21,22)(20,24,25,23)(26,28,31,39)(27,33,35,37)(29,38,43,54)(30,44,32,40)(34,47,50,52)(36,49,45,48)(41,57,51,53)(42,56,46,55);(26,29)(27,34)(28,38)(30,42)(31,43)(32,46)(33,47)(35,50)(36,51)(37,52)(39,54)(40,55)(41,45)(44,56)(48,57)(49,53);(18,20,21,25)(19,23,22,24)(27,35)(28,39)(34,50)(36,45)(38,54)(40,44)(41,51)(55,56);(26,30,31,32)(27,36,35,45)(28,40,39,44)(29,42,43,46)(33,48,37,49)(34,51,50,41)(38,55,54,56)(47,57,52,53)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54326);