Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33628 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C23×C17 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
534 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)(28,36)(29,40)(30,45)(31,33)(32,37)(34,43)(35,42)(38,56)(39,53)(41,51)(44,52)(46,50)(47,55)(48,57)(49,54);(18,20,21,25)(19,22,23,24);(26,28,31,39)(27,32,33,47)(29,41,44,57)(30,46,42,38)(34,50,49,56)(35,51,45,48)(36,52,53,40)(37,54,55,43);(27,33)(32,47)(34,49)(35,45)(36,53)(40,52)(48,51)(50,56)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26616);