Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(16,24)(17,21)(18,22)(19,23)(20,26)(25,29)(27,28)(32,38)(33,40)(35,42)(37,44)(39,41)(43,45);(14,16,19,26)(15,20,23,24)(17,25,18,27)(21,28,22,29)(30,31)(32,35)(33,37)(34,36)(38,42)(39,43)(40,44)(41,45);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,24,29)(30,32,34,39)(31,35,36,43)(33,41,40,38)(37,45,44,42);(14,18,19,17)(15,22,23,21)(16,25,26,27)(20,28,24,29);(15,23)(20,24)(21,22)(28,29)(31,36)(35,43)(37,44)(42,45)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54902);