Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10016 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #392 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,22,24,29)(17,25,27,20)(19,26,28,23)(30,31,35,39)(32,40,43,44)(33,38,34,37)(36,42,45,41);(14,16,18,24)(15,19,21,28)(17,26,27,23)(20,29,25,22)(30,32,35,43)(31,36,39,45)(33,42,34,41)(37,44,38,40);(19,28)(22,29)(31,37)(33,34)(36,44)(38,39)(40,45)(41,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3004);