Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11521 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#12807 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #410 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| socle | C2×C13 | #1799 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C8×C13 ◁ C2×C13×#131 ◁ G | |
428 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)(16,25)(17,29)(18,23,32,21)(19,24)(20,26)(22,31)(27,39,43,38)(28,40)(30,36,44,37)(33,41,34,45)(35,42);(14,16,17,26,19,28,31,42)(15,20,22,25,24,35,29,40)(18,27,30,41,32,43,44,45)(21,33,36,38,23,34,37,39);(15,21)(18,32)(20,33)(22,36)(23,24)(25,38)(27,43)(29,37)(30,44)(34,35)(39,40)(41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5795);