Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24473 |
| 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 | |
1314 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)(14,15,20,24,21,18,19,36)(16,25,28,22,30,39,29,27)(17,31,34,33,35,41,37,23)(26,43,44,40,45,38,32,42);(14,16)(15,22)(17,32)(18,27)(19,29)(20,28)(21,30)(23,40)(24,39)(25,36)(26,34)(31,38)(33,42)(35,44)(37,45)(41,43);(14,17)(15,23)(16,26)(18,33)(19,34)(20,37)(21,35)(22,38)(24,41)(25,42)(27,43)(28,32)(29,44)(30,45)(31,36)(39,40);(14,18,21,15)(16,27,30,22)(17,33,35,23)(19,24,20,36)(25,29,39,28)(26,43,45,38)(31,34,41,37)(32,42,44,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17461);