Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33799 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,20)(18,21)(19,24)(23,28)(25,27)(26,29)(30,31)(32,42)(33,41)(34,37)(35,48)(36,39)(38,45)(40,50)(43,58)(44,60)(46,53)(47,55)(49,57)(51,56)(52,59)(54,61);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(31,37)(32,43)(39,41)(40,53)(44,51)(45,59)(48,55)(49,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,32,34,43)(31,38,37,52)(33,44,36,51)(35,49,47,61)(39,54,41,57)(40,56,53,60)(42,55,58,48)(45,46,59,50);(15,21)(19,22)(20,29)(27,28)(30,33,34,36)(31,39,37,41)(32,44,43,51)(35,46,47,50)(38,54,52,57)(40,55,53,48)(42,56,58,60)(45,49,59,61)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26787);