Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C2×C13×#3561 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
7258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(4,7)(5,9)(11,12,15,16)(13,19,20,17)(14,22,23,18)(21,24,26,25);(4,7)(8,10)(12,16)(13,20)(18,22)(21,26);(3,4)(5,8)(6,7)(9,10)(11,12)(13,17)(14,18)(15,16)(19,20)(21,24)(22,23)(25,26);(3,5,6,9)(4,8,7,10)(11,13,15,20)(12,17,16,19)(14,21,23,26)(18,24,22,25);(11,14,15,23)(12,18,16,22)(13,21,20,26)(17,24,19,25)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55719);