Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C2×C13×#3400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C2×C13×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×Q8×C13 ◁ G | |
1970 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)(11,12,15,18)(13,19,20,26)(14,22,24,17)(16,23,25,21);(3,4,7,8)(5,9,6,10)(13,20)(16,25)(19,26)(21,23);(3,5,7,6)(4,9,8,10)(11,13,15,20)(12,16,18,25)(14,23,24,21)(17,26,22,19);(3,6,7,5)(4,9,8,10)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54385);