Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C42 |
| direct product | C13×#12594 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C13 | C42 |
| commutator | C4 | C2×C4×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C2×#97 |
| prime radical | C23×C13 | C2×M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C13 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,26,32,27,29,34,36,28,33,35,37,25,31,24,30);(15,18)(19,21)(23,29,33,31)(24,34)(26,35)(30,37,36,32);(14,16,17,20)(15,19,18,21)(22,24,25,35,28,34,27,26)(23,30,31,37,33,36,29,32)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5582);