Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#17812 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C22×C4⋊C4 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C4×C13×#41 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(17,20)(21,25)(22,26)(24,27)(28,29)(30,31,33,36,34,37,40,43)(32,35,39,42,38,41,44,45);(14,15,20,26,18,22,17,19)(16,21,27,29,23,28,24,25)(30,32)(31,35)(33,39)(34,38)(36,42)(37,41)(40,44)(43,45);(14,16)(15,21)(17,24)(18,23)(19,25)(20,27)(22,28)(26,29)(32,38)(35,41)(39,44)(42,45);(16,23)(21,28)(24,27)(25,29)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10800);