Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33922 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
488 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)(18,19,22,21)(20,24,25,23)(26,27,29,34)(28,37,38,32)(30,33,41,49)(31,44,42,36)(35,51,50,43)(39,45,54,48)(40,47,55,53)(46,57,52,56);(18,20)(19,23)(21,24)(22,25)(26,28)(27,32)(29,38)(30,39)(31,40)(33,48)(34,37)(35,46)(36,47)(41,54)(42,55)(43,57)(44,53)(45,49)(50,52)(51,56);(18,21,22,19)(20,24,25,23)(27,33)(28,38)(30,43)(31,42)(32,45)(34,49)(35,36)(37,48)(39,56)(41,51)(44,50)(46,53)(47,52)(54,57);(20,25)(23,24)(27,34)(28,38)(33,49)(35,50)(36,44)(39,54)(40,55)(56,57)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26910);