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×#24410 |
| 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 | |
1322 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)(16,24,27,20)(17,29,30,21)(18,23)(19,22)(25,32,36,28)(26,35)(31,42,43,37)(33,34)(38,41)(39,44)(40,45);(14,16,19,27)(15,20,22,24)(17,26,30,41)(18,32,34,28)(21,35,29,38)(23,25,33,36)(31,44,43,40)(37,39,42,45);(14,15)(16,25)(17,21)(18,33)(19,22)(20,32)(23,34)(24,28)(26,39)(27,36)(29,30)(31,42)(35,44)(37,43)(38,40)(41,45);(14,17)(15,21)(16,26)(18,31)(19,30)(20,35)(22,29)(23,37)(24,38)(25,39)(27,41)(28,40)(32,44)(33,42)(34,43)(36,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17398);