Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19025 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3561 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
872 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,22)(16,23,26,29)(17,21,18,27)(20,24,28,25)(30,31,34,37)(32,38,39,45)(33,41,42,36)(35,43,44,40);(14,16,19,26)(15,20,22,28)(17,25,18,24)(21,29,27,23)(33,42)(36,41)(38,45)(40,43);(14,15)(16,20)(17,21)(18,27)(19,22)(23,24)(25,29)(26,28)(30,32)(31,35)(33,43)(34,39)(36,45)(37,44)(38,41)(40,42);(14,17,19,18)(15,21,22,27)(16,24,26,25)(20,23,28,29)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12013);