Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#9875 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle, prime radical | C23×C13 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C43×C13 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
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)(16,20)(17,18)(19,21)(22,23,27,28,26,29,25,24)(30,31)(32,38)(33,42)(34,36)(35,40)(37,39)(41,44)(43,45);(15,18)(19,20)(22,24,25,29,26,28,27,23)(30,32,39,45,34,41,33,40)(31,35,42,44,36,43,37,38);(14,16,17,21)(15,19,18,20)(22,25,26,27)(23,28,29,24)(31,36)(35,43)(37,42)(38,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2863);