Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#11750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 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)(26,27,30,35,32,37,31,36)(28,38,41,51,39,54,42,55)(29,43,45,34,47,52,46,53)(33,44,49,40,48,57,50,56);(18,19)(20,23)(21,25)(22,24)(26,28)(27,33)(29,44)(30,42)(31,41)(32,39)(34,51)(35,50)(36,49)(37,48)(38,52)(40,46)(43,54)(45,56)(47,57)(53,55);(18,20,22,21)(19,23,24,25)(28,39)(33,48)(38,54)(40,56)(41,42)(44,57)(49,50)(51,55)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4738);