Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13310 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13310 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,27)(17,21)(18,26)(19,24)(20,25)(22,29)(23,31)(28,42)(30,41)(32,37)(33,36)(34,40)(35,43)(38,45)(39,44);(15,21)(17,31)(18,19)(22,38)(23,26)(24,37)(25,36)(27,42)(28,43)(29,34)(32,33)(35,40)(39,41)(44,45);(14,16)(15,22)(17,28)(18,34)(19,29)(20,30)(21,35)(23,39)(24,41)(25,40)(26,27)(31,43)(32,45)(33,44)(36,38)(37,42)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6298);