Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#17913 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C2×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
632 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)(14,15,19,23)(16,24,26,29)(17,22,18,21)(20,27,28,25)(30,31,33,37,34,36,40,43)(32,35,38,42,39,41,44,45);(14,16)(15,20)(17,25)(18,27)(19,26)(21,24)(22,29)(23,28);(30,32,33,38,34,39,40,44)(31,35,37,42,36,41,43,45);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,24,28,29)(31,36)(35,41)(37,43)(42,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10901);