Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C13 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G | |
1110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25)(17,29)(18,21)(19,24)(20,27)(22,32)(23,34)(26,40)(28,42)(30,37)(31,39)(33,43)(35,41)(36,44)(38,45);(14,16)(15,20)(17,30)(18,33)(19,26)(21,36)(22,40)(23,38)(24,37)(25,29)(27,32)(28,34)(31,44)(35,45)(39,42)(41,43);(15,21)(18,34)(20,36)(22,41)(23,24)(25,42)(28,33)(29,39)(31,35)(37,38)(40,43)(44,45);(16,26)(20,37)(25,40)(27,30)(28,33)(36,38)(42,43)(44,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26556);