Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1610 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)(17,33)(18,39)(19,43)(20,25)(21,26)(22,30)(23,37)(24,40)(28,56)(29,45)(31,47)(32,46)(34,54)(35,65)(36,51)(38,50)(41,53)(42,52)(44,58)(48,62)(49,68)(55,59)(57,74)(60,71)(61,70)(63,66)(64,69)(67,73)(72,77)(75,76);(14,16)(15,22)(17,34)(18,29)(19,31)(20,30)(21,32)(23,48)(24,45)(25,46)(26,47)(27,43)(28,36)(33,44)(35,64)(37,58)(38,62)(39,55)(40,61)(41,59)(42,60)(49,72)(50,56)(51,54)(52,70)(53,71)(57,67)(63,69)(65,74)(66,77)(68,76)(73,75);(14,17)(15,23)(16,28)(18,35)(19,36)(20,37)(21,38)(22,44)(24,49)(25,50)(26,51)(27,54)(29,57)(30,34)(31,62)(32,58)(33,43)(39,63)(40,66)(41,67)(42,68)(45,69)(46,48)(47,56)(52,73)(53,65)(55,74)(59,76)(60,77)(61,64)(70,72)(71,75);(14,18,21,42)(15,24,26,53)(16,29,32,60)(17,35,38,68)(19,41,20,40)(22,45,47,71)(23,49,51,65)(25,52,43,39)(27,55,46,70)(28,57,58,77)(30,61,31,59)(33,63,50,73)(34,64,62,76)(36,67,37,66)(44,69,56,75)(48,72,54,74)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16881);