Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12933 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12933 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1853 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
380 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,21,24,35)(16,25)(17,28)(18,19)(22,36,38,43)(23,40,33,29)(26,42)(27,32)(30,31)(34,39,45,37);(14,15,19,33,20,24,18,23)(16,22,25,37,27,38,32,39)(17,29,28,21,31,40,30,35)(26,43,41,34,42,36,44,45);(14,16)(15,22)(17,26)(18,32)(19,25)(20,27)(21,34)(23,39)(24,38)(28,41)(29,43)(30,44)(31,42)(33,37)(35,45)(36,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5921);