Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12953 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1864 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
416 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)(14,15,18,24,20,25,19,37)(16,26,29,41,31,38,30,45)(17,32,34,42,36,22,35,23)(21,33,39,27,40,44,43,28);(14,16)(15,21,25,40)(17,33)(18,30)(19,29)(20,31)(22,38,32,26)(23,41,42,45)(24,43,37,39)(27,35)(28,34)(36,44);(15,22)(17,34)(18,19)(21,38)(23,37)(24,42)(25,32)(26,40)(27,44)(28,33)(29,30)(35,36)(39,41)(43,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5941);