Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60761 |
| 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 ◁ C22×#41×C17 ◁ G | |
2140 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)(20,24)(21,23)(22,25)(26,27,32,36)(28,33,39,48)(29,41,43,49)(30,35,31,44)(34,45,50,42)(37,51,53,56)(38,47,40,54)(46,55,57,52);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,37)(30,38)(31,40)(32,39)(34,46)(35,47)(36,48)(41,51)(42,52)(43,53)(44,54)(45,55)(49,56)(50,57);(20,25)(22,24)(26,29)(27,34)(28,37)(30,42)(31,45)(32,43)(33,46)(35,49)(36,50)(38,52)(39,53)(40,55)(41,44)(47,56)(48,57)(51,54);(19,23)(22,24)(26,30,32,31)(27,35,36,44)(28,38,39,40)(29,42,43,45)(33,47,48,54)(34,49,50,41)(37,52,53,55)(46,56,57,51);(28,39)(33,48)(37,53)(38,40)(46,57)(47,54)(51,56)(52,55)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53749);