Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33858 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×#443 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,21)(16,26)(17,30)(18,19)(22,23)(24,40)(25,39)(27,44)(28,42)(29,35)(31,36)(33,34)(37,38)(41,43);(14,15,20,25)(16,27,29,22)(17,31,34,40)(18,24,19,36)(21,33,39,30)(23,42,44,28)(26,41,35,38)(32,43,45,37);(14,16)(15,22)(17,28)(18,35)(19,26)(20,29)(21,37)(23,40)(24,41)(25,27)(30,32)(31,44)(33,45)(34,42)(36,38)(39,43);(14,16)(15,23)(17,32)(18,26)(19,35)(20,29)(21,38)(22,40)(24,43)(25,44)(27,31)(28,30)(33,42)(34,45)(36,37)(39,41)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26846);