Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23874 |
| 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 | |
1674 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)(16,21)(17,28)(18,20)(19,24)(22,29)(23,31)(25,40)(26,35)(27,37)(30,39)(32,34)(33,38)(36,41)(42,44)(43,45);(15,20)(18,31)(21,35)(22,28)(23,24)(26,32)(29,33)(34,37)(36,40)(38,39)(41,43)(44,45);(14,16,19,27)(15,21,24,37)(17,25,30,42)(18,32,31,26)(20,34,23,35)(22,36,38,45)(28,44,39,40)(29,43,33,41);(14,17)(15,22)(16,25)(18,33)(19,30)(20,28)(21,36)(23,39)(24,38)(26,43)(27,42)(29,31)(32,41)(34,44)(35,40)(37,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16862);