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×#33896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3341 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ 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)(18,19,21,23)(20,24,25,22)(26,27,32,35)(28,33,31,47)(29,39,42,56)(30,43,46,55)(34,49,51,41)(36,38,52,45)(37,54,40,53)(44,48,57,50);(18,20)(19,22)(21,25)(23,24)(26,28,32,31)(27,33,35,47)(29,40,42,37)(30,38,46,45)(34,50,51,48)(36,43,52,55)(39,53,56,54)(41,57,49,44);(26,29,32,42)(27,34,35,51)(28,37,31,40)(30,44,46,57)(33,48,47,50)(36,53,52,54)(38,49,45,41)(39,55,56,43);(20,25)(22,24)(27,35)(33,47)(34,51)(36,52)(39,56)(43,55)(48,50)(53,54)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26884);