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×#33649 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C24×C17 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(26,27,32,37)(28,38,41,55)(29,36,31,34)(30,43,46,51)(33,48,50,40)(35,42,53,45)(39,56,47,52)(44,54,57,49);(19,22)(23,25);(18,20,21,24)(19,23,22,25)(26,28)(27,33)(29,39)(30,44)(31,47)(32,41)(34,49)(35,52)(36,54)(37,50)(38,43)(40,45)(42,48)(46,57)(51,55)(53,56);(26,29,32,31)(27,34,37,36)(28,39,41,47)(30,42,46,45)(33,49,50,54)(35,51,53,43)(38,52,55,56)(40,44,48,57)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26637);