Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60753 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60868 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C2×C13×#540 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#117 ◁ G | |
1754 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)(32,40)(33,34)(36,43)(38,39)(41,42)(44,45);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,31)(32,36)(33,38)(34,39)(35,37)(40,43)(41,44)(42,45);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,32)(31,36)(33,40)(34,42)(35,41)(37,44)(38,43)(39,45);(15,21)(19,22)(20,29)(27,28)(31,37)(36,44)(38,39)(43,45);(30,33,35,34)(31,38,37,39)(32,40,41,42)(36,43,44,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53856);