Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C16 · Schur multiplier (H2) = C23 |
| direct product | C13×#13558 |
| subgroup | G/H | |
|---|---|---|
| center | C13×C16 | C2×D4 |
| commutator | C4 | C22×C13×C16 |
| Frattini, cosocle | C2×C16 | C23×C13 |
| socle | C2×C13 | C2×C22⋊C16 |
| prime radical | C2×C13×#41 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C13×C16 ◁ C22×C13×C16 ◁ G | |
290 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)(14,15,18,25,19,26,37,52,20,27,38,53,40,54,65,74,21,23,39,46,41,47,66,70,17,24,34,49,35,50,62,72)(16,28,30,55,31,56,59,75,29,43,57,51,58,68,76,73,32,48,36,63,60,71,64,77,33,22,42,44,61,45,67,69);(14,16)(15,22)(17,33)(18,36)(19,31)(20,29)(21,32)(23,43)(24,48)(25,51)(26,45)(27,28)(30,39)(34,57)(35,61)(37,64)(38,42)(40,58)(41,60)(44,46)(47,68)(49,55)(50,71)(52,73)(53,63)(54,56)(59,66)(62,76)(65,67)(69,70)(72,75)(74,77);(15,23)(22,43)(24,27)(25,46)(26,47)(28,48)(44,51)(45,68)(49,53)(50,54)(52,70)(55,63)(56,71)(69,73)(72,74)(75,77)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6546);