Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C4 |
| direct product | C13×#13106 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C2×D4 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C8×D4 |
| prime radical | C23×C13 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C22×C13×C16 ◁ G | |
272 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
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)(16,19)(17,18)(20,21)(22,23,28,33,27,34,44,51,26,31,43,35,42,32,49,50)(24,25,38,40,37,41,48,53,36,29,45,46,52,39,30,47);(15,18)(19,21)(22,24,28,38,27,37,44,48,26,36,43,45,42,52,49,30)(23,29,33,46,34,39,51,47,31,25,35,40,32,41,50,53);(14,16,17,20)(15,19,18,21)(22,25,26,29)(23,30,31,48)(24,35,36,33)(27,41,42,39)(28,40,43,46)(32,45,34,38)(37,50,52,51)(44,53,49,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6094);