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×#24409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1336 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)(17,28)(18,22)(19,23)(21,30)(25,42,43,35)(26,40,33,36)(29,45,44,37)(31,41)(32,39)(34,38);(14,16)(15,20)(17,29)(18,27)(19,33)(21,37)(22,24)(23,40)(25,31)(26,32)(28,45)(30,44)(34,43)(35,38)(36,39)(41,42);(14,17)(15,21)(16,25)(18,30)(19,34)(20,35)(22,28)(23,41)(24,42)(26,44)(27,43)(29,33)(31,32)(36,45)(37,40)(38,39);(14,16)(15,20)(17,25)(18,27)(19,26)(21,35)(22,24)(23,36)(28,42)(29,31)(30,43)(32,33)(34,44)(37,38)(39,40)(41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17397);