Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2404 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
1164 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)(14,15)(16,20)(17,21)(18,23)(19,24)(22,26)(25,36)(27,34)(28,45)(29,37)(30,38)(31,40)(32,41)(33,42)(35,44)(39,43);(14,16)(15,20)(17,28,29,44)(18,27)(19,26)(21,35,37,45)(22,24)(23,34)(25,30,42,31)(32,43)(33,38,36,40)(39,41);(14,17)(15,21)(16,25)(18,31)(19,29)(20,33)(22,36)(23,40)(24,37)(26,42)(27,44)(28,43)(30,32)(34,45)(35,39)(38,41);(14,16)(15,22)(17,25)(18,27)(19,26)(20,24)(21,36)(23,39)(28,30)(29,42)(31,44)(32,43)(33,37)(34,41)(35,40)(38,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16983);