Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33392 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×#102 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#576 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
1154 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)(14,15,18,23,19,25,33,24)(16,21,28,38,26,36,41,39)(17,29,31,22,32,20,30,35)(27,42,44,37,40,34,43,45);(15,20)(17,30)(18,33)(21,34)(22,23)(24,35)(25,29)(27,43)(28,41)(31,32)(36,42)(37,38)(39,45)(40,44);(14,16)(15,21)(17,27)(18,28)(19,26)(20,34)(22,37)(23,38)(24,39)(25,36)(29,42)(30,43)(31,44)(32,40)(33,41)(35,45);(16,26)(21,36)(27,40)(28,41)(34,42)(37,45)(38,39)(43,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26380);