Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13289 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#102 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,18)(19,21)(22,23,27,34,29,35,28,33)(24,36,41,53,42,52,40,48)(25,43,37,31,44,32,26,45)(30,47,49,39,51,38,50,46);(15,18)(19,20)(22,24,37,39,28,41,25,38,29,42,26,46,27,40,44,47)(23,30,32,52,34,50,45,53,35,51,43,36,33,49,31,48);(14,16,17,21)(15,19,18,20)(22,25,27,37,29,44,28,26)(23,31,33,43,35,45,34,32)(24,38,40,39,42,47,41,46)(30,48,49,36,51,53,50,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6277);