Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#12667 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1770 |
| prime radical | C23×C13 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C2×C13×M32 ◁ G | |
296 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)(14,15,19,24,20,25,34,40,18,23,31,39,33,17,22,32)(16,21,27,36,28,37,42,45,29,26,35,41,43,30,38,44);(14,16)(15,21,23,26)(17,30,25,37)(18,29)(19,27)(20,28)(22,38)(24,36,39,41)(31,35)(32,44,40,45)(33,43)(34,42);(14,17,31,40,20,15,22,39,18,25,19,32,33,23,34,24)(16,26,27,41,28,30,42,44,29,21,35,36,43,37,38,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5655);