Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33691 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33693 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×#405 ◁ G | |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25)(16,21,27,43)(17,30,32,65)(18,35,38,70)(19,41,39,24)(22,46,48,33)(23,50,53,40)(26,54,56,64)(28,59,36,69)(29,62,58,45)(31,52,34,68)(37,47,66,49)(42,67,74,57)(44,72,51,61)(55,77,63,75)(60,76,71,73);(14,16,20,27)(15,21,25,43)(17,26,32,56)(18,36,38,28)(19,29,39,58)(22,42,48,74)(23,51,53,44)(24,45,41,62)(30,64,65,54)(31,63,34,55)(33,67,46,57)(35,69,70,59)(37,71,66,60)(40,72,50,61)(47,76,49,73)(52,77,68,75);(14,17)(15,22)(16,26)(18,37)(19,31)(20,32)(21,42)(23,52)(24,47)(25,48)(27,56)(28,60)(29,63)(30,35)(33,40)(34,39)(36,71)(38,66)(41,49)(43,74)(44,75)(45,76)(46,50)(51,77)(53,68)(54,59)(55,58)(57,61)(62,73)(64,69)(65,70)(67,72);(16,27)(17,31,32,34)(18,38)(21,43)(22,47,48,49)(23,53)(26,55,56,63)(29,58)(30,52,65,68)(33,37,46,66)(35,70)(40,50)(42,73,74,76)(45,62)(54,77,64,75)(57,71,67,60)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26681);