Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C2×Q8×C13×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| socle | C23×C13 | C25 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
7522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4,5,6)(7,10,9,8);(3,7,5,9)(4,8,6,10);(11,12)(13,16)(14,15)(17,18);(12,15)(16,18);(11,13,14,17)(12,16,15,18)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55701);