Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23897 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1718 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)(17,27)(18,30)(19,23)(21,29)(22,32)(24,39)(25,42)(26,35)(28,38)(31,37)(33,41)(34,44)(36,43)(40,45);(14,16,19,26)(15,20,23,35)(17,24,28,40)(18,25,32,44)(21,36,37,33)(22,34,30,42)(27,45,38,39)(29,41,31,43);(14,17)(15,21)(16,24)(18,31)(19,28)(20,33)(22,38)(23,37)(25,43)(26,40)(27,30)(29,32)(34,45)(35,36)(39,42)(41,44);(18,32)(22,30)(25,44)(27,38)(29,31)(34,42)(39,45)(41,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16886);