Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| prime radical | C13×#3444 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25)(16,23,18,21)(17,27,26,22)(19,24,28,29)(32,38)(35,42)(39,44)(43,45);(14,16,20,18)(15,21,25,23)(17,28,26,19)(22,29,27,24)(30,31,34,37)(32,35,38,42)(33,40,41,36)(39,45,44,43);(14,17)(15,22)(16,19)(18,28)(20,26)(21,24)(23,29)(25,27)(30,32)(31,35)(33,39)(34,38)(36,43)(37,42)(40,45)(41,44);(14,18,20,16)(15,23,25,21)(17,28,26,19)(22,29,27,24);(14,19,20,28)(15,24,25,29)(16,26,18,17)(21,27,23,22)(30,33,34,41)(31,36,37,40)(32,39,38,44)(35,43,42,45);(14,15)(16,21)(17,22)(18,23)(19,24)(20,25)(26,27)(28,29)(30,32)(31,35)(33,39)(34,38)(36,43)(37,42)(40,45)(41,44)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55825);