Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#17970 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C13×#3169 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C13×#431 ◁ G | |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(22,25)(23,28)(24,26)(27,29)(30,31,35,38,34,37,43,45)(32,39,41,42,40,36,44,33);(15,19)(17,25)(20,26)(21,22)(24,29)(27,28)(30,32)(31,36)(33,38)(34,40)(35,41)(37,39)(42,45)(43,44);(14,16)(15,20)(17,24)(18,23)(19,26)(21,28)(22,27)(25,29)(30,33,35,39,34,42,43,36)(31,32,38,41,37,40,45,44);(15,21)(16,23)(19,22)(24,29)(31,37)(32,40)(38,45)(41,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10958);