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×#61210 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#532 ◁ G | |
2014 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)(26,27,32,36)(28,33,39,49)(29,40,42,50)(30,35,31,44)(34,45,51,41)(37,52,55,57)(38,47,43,48)(46,53,56,54);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,37)(30,43)(31,38)(32,39)(34,46)(35,48)(36,49)(40,52)(41,54)(42,55)(44,47)(45,53)(50,57)(51,56);(26,29,32,42)(27,34,36,51)(28,37,39,55)(30,41,31,45)(33,46,49,56)(35,50,44,40)(38,53,43,54)(47,52,48,57);(20,25)(22,24)(26,28)(27,33)(29,37)(30,43)(31,38)(32,39)(34,46)(35,48)(36,49)(40,52)(41,54)(42,55)(44,47)(45,53)(50,57)(51,56);(26,30,32,31)(27,35,36,44)(28,38,39,43)(29,41,42,45)(33,47,49,48)(34,50,51,40)(37,53,55,54)(46,52,56,57)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54198);