Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#7860 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C13 | C42 |
| commutator | C4 | C2×C4×C8×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | C2×#95 |
| prime radical | C24×C13 | C4⋊C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C13 ◁ G | |
666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20,18,21,16,19)(22,23)(24,31,33,37)(25,29)(26,35)(27,30)(28,32,36,34);(22,24,26,34,27,33,25,32)(23,28,29,31,30,36,35,37);(14,16,18,17)(15,19,21,20)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 848);