Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C8×C13×#106 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | D4 |
| commutator | C4 | C2×C4×C8×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle, prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8)(21,22,23,24,25,26,27,28,29,30,31,32,33);(9,10,11,12)(14,17)(15,19)(18,20);(13,14,15,17,16,18,19,20)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1268);