Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12918 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #120 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1850 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
376 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,25,20,24,36,41,21,26,37,42,18,28,35,43)(16,27,30,33,23,22,38,34,31,39,45,32,29,40,44,17);(14,16,19,30,20,23,36,38,21,31,37,45,18,29,35,44)(15,22,25,34,24,39,41,32,26,40,42,17,28,27,43,33);(14,17)(15,23)(16,28)(18,32)(19,27)(20,33)(21,34)(22,36)(24,31)(25,38)(26,29)(30,43)(35,40)(37,39)(41,45)(42,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5906);