Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C13×#3218 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G | |
2146 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);(3,4)(5,9)(6,8)(7,10)(11,12)(13,19)(14,16)(15,23)(17,21)(18,22)(20,26)(24,25);(3,5,6,10)(4,7,8,9)(12,16)(17,25)(18,23)(19,26);(5,10)(7,9)(11,13,14,20)(12,17,16,25)(15,24,22,21)(18,26,23,19);(4,8)(7,9)(12,16)(17,25)(18,23)(19,26)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53774);