Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C2×C13×#3393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×Q8×C13 ◁ G | |
1958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(4,8)(9,10)(11,12)(13,16)(14,17)(15,19)(18,22)(20,23)(21,25)(24,26);(3,4,7,8)(5,9,6,10)(11,13,15,21)(12,16,19,25)(14,20,22,26)(17,23,18,24);(3,5,7,6)(4,9,8,10)(12,17)(14,22)(16,23)(18,19)(20,26)(24,25);(3,6,7,5)(4,9,8,10)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54377);