Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19158 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×#121 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
596 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)(14,15,18,21)(16,22,24,29)(17,26,23,20)(19,27,28,25)(30,31)(32,39)(33,37)(34,42)(35,38)(36,40)(41,44)(43,45);(14,16,23,27,18,24,17,25)(15,19,26,29,21,28,20,22);(16,24)(19,28)(22,29)(25,27)(30,32)(31,36)(33,40)(34,43)(35,41)(37,44)(38,45)(39,42);(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12146);