Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13005 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13006 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1874 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
472 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)(14,15,20,26,45,48,43,24,21,27,42,61,19,25,18,40)(16,28,32,22,44,51,30,59,33,63,72,52,31,57,46,50)(17,34,37,53,36,56,41,60,39,55,47,58,38,23,35,54)(29,64,67,73,66,74,65,49,69,76,71,75,68,62,70,77);(14,16,19,44,21,33,45,31)(15,22,48,50,27,52,25,59)(17,29,38,66,39,69,36,68)(18,32,42,30,43,72,20,46)(23,49,34,73,56,77,55,75)(24,57,61,63,40,51,26,28)(35,67,47,65,41,71,37,70)(53,64,60,62,58,76,54,74);(14,17)(15,23)(16,29)(18,41)(19,38)(20,47)(21,39)(22,49)(24,58)(25,55)(26,60)(27,56)(28,62)(30,70)(31,68)(32,71)(33,69)(34,48)(35,43)(36,45)(37,42)(40,53)(44,66)(46,65)(50,73)(51,64)(52,77)(54,61)(57,76)(59,75)(63,74)(67,72)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5994);