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×#33647 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
584 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)(28,32)(29,33)(30,43)(31,34)(35,40)(36,41)(37,44)(38,53)(39,45)(42,48)(46,50)(47,51)(49,54)(52,55)(56,57);(19,22)(23,25)(26,28,31,39)(27,32,34,45)(29,37,42,52)(30,38,41,51)(33,44,48,55)(35,46,49,56)(36,47,43,53)(40,50,54,57);(18,20,21,24)(19,23,22,25)(27,33)(29,40)(30,41)(32,44)(34,48)(35,36)(37,50)(38,51)(42,54)(43,49)(45,55)(46,47)(52,57)(53,56);(27,34)(32,45)(33,48)(35,49)(36,43)(44,55)(46,56)(47,53)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26635);