Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12682 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×C22⋊C4 |
| commutator | C23 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C2×C22⋊C8 |
| prime radical | C22×C13×#41 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C8×C13 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,26,22,27,33,41,23,25,34,38,35,39,46,48)(20,28,30,40,31,42,44,49,29,24,32,36,43,37,45,47);(18,20)(19,24)(21,32)(22,31)(23,29)(25,28)(26,40)(27,37)(30,34)(33,45)(35,43)(36,38)(39,42)(41,49)(44,46)(47,48);(15,17)(20,29)(24,28)(30,32)(31,43)(36,40)(37,42)(44,45)(47,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5670);