Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23882 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23885 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1662 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)(16,27)(17,32)(18,35)(19,25)(20,24)(21,26)(22,30)(23,34)(28,37)(29,38)(31,41)(33,40)(36,39)(42,44)(43,45);(14,16)(15,22)(17,28)(18,29)(19,36)(20,30)(21,31)(23,38)(24,41)(25,27)(26,39)(32,42)(33,45)(34,44)(35,43)(37,40);(14,17,21,18)(15,23,26,40)(16,28,31,29)(19,34,20,33)(22,37,39,38)(24,32,25,35)(27,42,41,43)(30,45,36,44);(14,18,21,17)(15,23,26,40)(16,29,31,28)(19,33,20,34)(22,38,39,37)(24,32,25,35)(27,43,41,42)(30,44,36,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16873);