Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61066 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×D4×C13 ◁ G | |
2912 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,25)(20,26,28,32)(21,30,31,24)(23,27,33,29);(18,20)(19,23)(21,27)(22,28)(24,32)(25,33)(26,30)(29,31);(15,17);(20,27)(21,31)(23,32)(24,30)(26,33)(28,29);(20,28)(23,33)(26,32)(27,29)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54054);