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×#23873 |
| 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 | |
1686 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)(16,24)(17,28)(18,31)(19,23)(20,26)(21,29)(22,33)(25,36)(27,38)(30,39)(32,35)(34,37)(40,41)(42,44)(43,45);(14,16,19,27)(15,20,23,35)(17,25,30,42)(18,32,33,26)(21,36,37,44)(22,38,31,24)(28,40,39,45)(29,43,34,41);(18,33)(20,35)(22,31)(26,32)(28,39)(29,34)(36,44)(41,43);(14,17)(15,21)(16,25)(18,34)(19,30)(20,36)(22,39)(23,37)(24,40)(26,43)(27,42)(28,31)(29,33)(32,41)(35,44)(38,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16861);