Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#578 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
1086 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,29)(20,30,34,58)(21,26,35,49)(22,38,42,56)(23,43,40,28)(25,45,48,32)(27,52,54,41)(31,57,59,79)(33,62,44,53)(36,65,63,78)(37,68,64,51)(39,55,70,47)(46,71,72,60)(50,75,74,67)(61,80,69,76)(66,77,81,73);(18,20,24,34)(19,25,29,48)(21,31,35,59)(22,39,42,70)(23,44,40,33)(26,46,49,72)(27,53,54,62)(28,55,43,47)(30,56,58,38)(32,52,45,41)(36,66,63,81)(37,69,64,61)(50,76,74,80)(51,77,68,73)(57,78,79,65)(60,75,71,67);(15,17)(18,21)(19,26)(20,31)(22,36)(23,37)(24,35)(25,46)(27,50)(28,51)(29,49)(30,57)(32,60)(33,61)(34,59)(38,65)(39,66)(40,64)(41,67)(42,63)(43,68)(44,69)(45,71)(47,73)(48,72)(52,75)(53,76)(54,74)(55,77)(56,78)(58,79)(62,80)(70,81);(21,35)(26,49)(31,59)(36,63)(37,64)(46,72)(50,74)(51,68)(57,79)(60,71)(61,69)(65,78)(66,81)(67,75)(73,77)(76,80)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26513);