Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13318 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13318 |
| 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 | |
532 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)(17,31)(18,26)(19,24)(20,25)(21,28)(22,29)(23,35)(30,43)(32,44)(33,39)(34,40)(36,42)(37,41)(38,45);(14,16)(15,21)(17,32)(18,29)(19,37)(20,30)(22,40)(23,41)(24,38)(25,39)(26,44)(27,31)(28,35)(33,34)(36,45)(42,43);(14,16)(15,22)(17,33)(18,37)(19,29)(20,30)(21,23)(24,43)(25,41)(26,27)(28,36)(31,38)(32,34)(35,45)(39,40)(42,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6306);