Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#23744 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C22×D4 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C22×C42×C13 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(16,21,17,19)(22,23)(24,26)(25,27)(28,29);(14,16,18,17)(15,19,20,21)(22,24,25,28)(23,26,27,29)(30,31)(32,39)(33,37)(34,42)(35,38)(36,40)(41,44)(43,45);(14,17,18,16)(15,19,20,21)(23,27)(26,29)(30,32)(31,36)(33,40)(34,43)(35,41)(37,44)(38,45)(39,42);(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16732);