Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13397 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
390 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)(14,15,21,27)(16,22,31,47)(17,32,34,66)(18,38,42,54)(19,26,20,25)(23,48,50,35)(24,40,55,41)(28,57,58,77)(29,60,63,76)(30,56,43,46)(33,68,64,65)(36,67,37,53)(39,52,70,51)(44,72,73,59)(45,71,74,62)(49,69,75,61);(14,16)(15,22)(17,33)(18,29)(19,43)(20,30)(21,31)(23,49)(24,45)(25,56)(26,46)(27,47)(28,36)(32,65)(34,64)(35,69)(37,58)(38,60)(39,59)(40,71)(41,62)(42,63)(44,51)(48,61)(50,75)(52,73)(53,57)(54,76)(55,74)(66,68)(67,77)(70,72);(14,17,20,36,21,34,19,37)(15,23,26,51,27,50,25,52)(16,28,30,64,31,58,43,33)(18,39,41,48,42,70,40,35)(22,44,46,75,47,73,56,49)(24,53,38,66,55,67,54,32)(29,61,62,72,63,69,71,59)(45,68,60,77,74,65,76,57)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6385);