Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61701 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3506 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×D4×C13 ◁ G | |
1778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,20)(18,21)(19,24)(23,28)(25,27)(26,29)(30,31)(32,36)(33,40)(34,42)(35,38)(37,39)(41,44)(43,45);(14,16)(15,19)(17,23)(18,24)(20,26)(21,22)(25,29)(27,28)(30,32,35,34)(31,36,38,42)(33,39,41,43)(37,44,45,40);(14,17,18,25)(15,20,21,27)(16,23,24,29)(19,26,22,28)(30,33,35,41)(31,37,38,45)(32,39,34,43)(36,44,42,40);(16,24)(19,22)(23,29)(26,28)(30,32,35,34)(31,36,38,42)(33,39,41,43)(37,44,45,40);(15,21)(19,22)(20,27)(26,28)793 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54689);