Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#17919 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C13×#121 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C13×#431 ◁ G | |
596 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)(17,24)(20,26)(21,25)(23,28)(27,29)(30,31,33,37,34,36,40,43)(32,35,38,42,39,41,44,45);(14,15,18,21)(16,20,22,27)(17,25,24,19)(23,29,28,26);(14,16)(15,20)(17,23)(18,22)(19,26)(21,27)(24,28)(25,29)(30,32,33,38,34,39,40,44)(31,35,37,42,36,41,43,45);(16,22)(20,27)(23,28)(26,29)(31,36)(35,41)(37,43)(42,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10907);