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×#33970 |
| 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×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
528 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)(19,23)(24,25)(26,27)(28,37)(29,34)(30,33)(31,44)(32,38)(35,43)(36,42)(39,45)(40,47)(41,49)(46,55)(48,53)(50,57)(51,56)(52,54);(18,19,22,23)(20,24,21,25)(26,28,29,38)(27,32,34,37)(30,39,41,53)(31,40,42,54)(33,48,49,45)(35,46,50,51)(36,47,44,52)(43,56,57,55);(18,20,22,21)(19,24,23,25)(27,33)(28,38)(30,43)(31,42)(32,45)(34,49)(35,36)(37,48)(39,55)(41,57)(44,50)(46,52)(47,51)(53,56);(18,21,22,20)(19,24,23,25)(28,38)(32,37)(39,53)(40,54)(45,48)(46,51)(47,52)(55,56)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26958);