Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12833 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1807 |
| 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 | |
358 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)(16,27,31,45)(17,32,34,42)(18,28)(19,24)(20,26)(21,29,35,22)(23,36)(25,38)(30,44,39,33)(37,40)(41,43);(14,16,18,29,19,30,36,42,20,31,37,22,38,39,43,32)(15,21,23,27,25,17,28,33,26,35,41,45,24,34,40,44);(14,17)(15,22)(16,28)(18,33)(19,35)(20,34)(21,38)(23,39)(24,42)(25,32)(26,29)(27,43)(30,41)(31,40)(36,45)(37,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5821);