Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,32)(21,39)(22,29)(23,28)(24,41)(25,44)(26,31)(27,34)(30,42)(33,35)(36,48)(37,40)(38,49)(43,47)(45,46);(18,20,26,38)(19,27,31,48)(21,40,28,46)(22,35,24,43)(23,34,39,36)(25,45,42,37)(29,32,41,49)(30,33,44,47);(15,17)(18,21,22,30,42,29,39,19,26,28,24,44,25,41,23,31)(20,33,34,40,45,48,43,49,38,47,36,46,37,27,35,32)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6434);