Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23993 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1152 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)(14,15,18,20)(16,21,26,33)(17,27,28,22)(19,31,30,23)(24,34,32,36)(25,35,39,40)(29,37,42,41)(38,44,43,45);(15,20)(16,24,26,32)(21,34,33,36)(22,27)(23,31)(25,38,39,43)(35,44,40,45)(37,41);(14,16)(15,21)(17,25)(18,26)(19,32)(20,33)(22,35)(23,34)(24,30)(27,40)(28,39)(29,43)(31,36)(37,44)(38,42)(41,45);(14,17)(15,22)(16,25)(18,28)(19,29)(20,27)(21,35)(23,37)(24,38)(26,39)(30,42)(31,41)(32,43)(33,40)(34,44)(36,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16981);