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) = C2×C4 |
| direct product | C13×#12664 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C13×C16 | D4 |
| commutator | C4 | C2×C4×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C8×D4 |
| prime radical | C23×C13 | #131 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13×C16 ◁ C22×C13×C16 ◁ G | |
334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,23,28,24,29,41,38,25,30,42,37,22,27,36,21)(20,31,34,32,33,45,48,47,35,46,40,49,39,26,43,44);(14,15,16,17)(18,20)(19,26)(21,32)(22,39)(23,40)(24,33)(25,35)(27,46)(28,47)(29,31)(30,45)(34,42)(36,48)(37,44)(38,49)(41,43);(18,21,36,27,22,37,42,30,25,38,41,29,24,28,23,19)(20,32,48,46,39,44,34,45,35,49,43,31,33,47,40,26)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5652);