Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25406 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
884 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23,26,30,27,31,40,47)(24,28,33,42,34,43,51,53)(25,35,37,45,38,46,39,29)(32,48,49,44,36,52,50,41);(18,19,21,20)(22,24,26,33,27,34,40,51)(23,28,30,42,31,43,47,53)(25,36,37,50,38,32,39,49)(29,44,35,52,45,41,46,48);(22,25,27,38)(23,29,31,45)(24,32,34,36)(26,39,40,37)(28,41,43,44)(30,46,47,35)(33,50,51,49)(42,52,53,48);(18,20,21,19)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18394);