Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33583 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,24,29)(20,30,33,47)(21,28,23,26)(22,35,38,43)(25,40,42,32)(27,34,45,37)(31,48,39,44)(36,46,49,41);(14,15,16,17);(18,20)(19,25)(21,31)(22,36)(23,39)(24,33)(26,41)(27,44)(28,46)(29,42)(30,35)(32,37)(34,40)(38,49)(43,47)(45,48);(18,21,24,23)(19,26,29,28)(20,31,33,39)(22,34,38,37)(25,41,42,46)(27,43,45,35)(30,44,47,48)(32,36,40,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26571);