Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#25494 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C23×C17 | C2×#41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,25)(20,24,21,23)(26,27,32,46,30,35,31,36)(28,37,47,49,39,33,40,53)(29,41,45,34,43,52,44,51)(38,54,56,50,42,57,55,48);(18,20,22,21)(19,23,25,24)(26,28,32,47,30,39,31,40)(27,33,46,53,35,37,36,49)(29,42,45,55,43,38,44,56)(34,50,52,57,51,48,41,54);(26,29,30,43)(27,34,35,51)(28,38,39,42)(31,45,32,44)(33,48,37,50)(36,52,46,41)(40,56,47,55)(49,54,53,57);(18,21,22,20)(19,24,25,23)(27,35)(33,37)(34,51)(36,46)(41,52)(48,50)(49,53)(54,57)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18482);