Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13334 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13335 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2011 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,31)(18,36)(19,42)(20,24)(21,28)(22,33)(23,40)(25,39)(27,45)(29,67)(30,59)(32,50)(34,72)(35,49)(37,55)(38,56)(41,57)(43,52)(44,53)(46,66)(47,73)(48,63)(51,71)(54,64)(58,61)(60,69)(62,77)(65,75)(68,76)(70,74);(14,16,20,30)(15,21,24,46)(17,27,35,63)(18,37,41,73)(19,43,39,29)(22,48,50,45)(23,52,54,67)(25,55,42,47)(26,57,59,36)(28,64,66,40)(31,69,49,58)(32,70,33,65)(34,68,44,62)(38,61,71,60)(51,76,56,77)(53,74,72,75);(14,17)(15,22)(16,27)(18,38)(19,44)(20,35)(21,45)(23,53)(24,50)(25,56)(26,58)(28,65)(29,68)(30,63)(31,36)(32,64)(33,40)(34,39)(37,61)(41,71)(42,51)(43,62)(46,48)(47,77)(49,57)(52,75)(54,72)(55,76)(59,69)(60,73)(66,70)(67,74)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6323);