Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33684 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#117 ◁ C17×#405 ◁ G | |
546 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)(20,23)(21,22)(24,25)(26,27)(28,37)(29,34)(30,33)(31,44)(32,38)(35,43)(36,42)(39,50)(40,47)(41,48)(45,53)(46,57)(49,56)(51,55)(52,54);(19,22)(23,25)(26,28,29,38)(27,32,34,37)(30,39,41,53)(31,40,42,54)(33,45,48,50)(35,46,49,51)(36,47,44,52)(43,55,56,57);(27,33)(30,43)(31,42)(32,45)(34,48)(35,36)(37,50)(39,55)(40,54)(41,56)(44,49)(46,47)(51,52)(53,57);(18,20,21,24)(19,23,22,25)(28,38)(32,37)(39,53)(40,54)(45,50)(46,51)(47,52)(55,57)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26672);