Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1364 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)(16,24,26,20)(17,21)(18,23)(19,22)(25,34,43,42)(27,40,31,35)(28,36,44,45)(29,38)(30,37)(32,41)(33,39);(14,16)(15,20)(17,28)(18,31)(19,26)(21,36)(22,24)(23,40)(25,30)(27,33)(29,44)(32,43)(34,37)(35,39)(38,45)(41,42);(14,17)(15,21)(16,25)(18,32)(19,29)(20,34)(22,38)(23,41)(24,42)(26,43)(27,44)(28,31)(30,33)(35,45)(36,40)(37,39);(14,16)(15,20)(17,25)(18,27)(19,26)(21,34)(22,24)(23,35)(28,30)(29,43)(31,33)(32,44)(36,37)(38,42)(39,40)(41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17396);