Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33741 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C23×C13 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 85 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)(24,29,35,48)(25,38,42,67)(26,43,45,71)(27,46,44,32)(30,51,53,40)(31,54,55,39)(34,56,58,78)(36,63,61,84)(37,64,62,50)(41,70,69,66)(47,72,73,59)(49,76,75,57)(52,68,65,77)(60,83,82,80)(74,81,79,85);(15,18)(19,21)(22,24,28,35)(23,29,33,48)(25,34,42,58)(26,36,45,61)(27,37,44,62)(30,47,53,73)(31,49,55,75)(32,50,46,64)(38,56,67,78)(39,57,54,76)(40,59,51,72)(41,60,69,82)(43,63,71,84)(52,74,65,79)(66,80,70,83)(68,81,77,85);(22,25,39,68,27,41,45,51,28,42,54,77,44,69,26,40)(23,30,43,66,32,52,55,67,33,53,71,70,46,65,31,38)(24,34,57,81,37,60,61,72,35,58,76,85,62,82,36,59)(29,47,63,80,50,74,75,78,48,73,84,83,64,79,49,56);(14,16,17,20)(15,19,18,21)(24,35)(29,48)(34,58)(36,61)(37,62)(47,73)(49,75)(50,64)(56,78)(57,76)(59,72)(60,82)(63,84)(74,79)(80,83)(81,85)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26729);