Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1270 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)(16,27)(17,32)(18,38)(19,42)(20,25)(21,26)(22,30)(23,36)(24,39)(28,44)(29,57)(31,46)(33,48)(34,49)(35,51)(37,50)(40,52)(41,66)(43,47)(45,59)(53,58)(54,72)(55,69)(56,70)(60,62)(61,76)(63,65)(64,73)(67,71)(68,74)(75,77);(14,16,19,30,21,31,20,43)(15,22,25,27,26,47,42,46)(17,33,35,28,37,55,36,56)(18,29,39,58,41,59,40,67)(23,48,50,70,51,69,32,44)(24,45,38,53,52,57,66,71)(34,61,62,54,64,74,63,75)(49,72,65,76,73,77,60,68);(14,17)(15,23)(16,28)(18,34)(19,35)(20,36)(21,37)(22,44)(24,49)(25,50)(26,51)(27,48)(29,54)(30,55)(31,56)(32,42)(33,43)(38,65)(39,62)(40,63)(41,64)(45,68)(46,69)(47,70)(52,73)(53,72)(57,76)(58,74)(59,75)(60,66)(61,67)(71,77);(14,18,20,40,21,41,19,39)(15,24,42,66,26,52,25,38)(16,29,43,67,31,59,30,58)(17,34,36,63,37,64,35,62)(22,45,46,71,47,57,27,53)(23,49,32,60,51,73,50,65)(28,54,33,61,56,75,55,74)(44,68,69,77,70,76,48,72)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17284);