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×#23883 |
| 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 | |
1696 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)(16,26)(17,30)(18,23)(19,24)(20,25)(21,28)(22,32)(27,35)(29,40)(31,39)(33,38)(34,36)(37,43)(41,42)(44,45);(14,16)(15,21)(17,27)(18,34)(19,28)(20,29)(22,37)(23,26)(24,40)(25,36)(30,41)(31,44)(32,42)(33,43)(35,39)(38,45);(14,17,20,33)(15,22,25,39)(16,27,29,43)(18,32,19,31)(21,35,36,37)(23,38,24,30)(26,41,40,45)(28,44,34,42);(15,23)(18,19)(21,26)(22,38)(24,25)(28,34)(30,39)(31,32)(35,41)(36,40)(37,45)(42,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16871);