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×#62838 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6518 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)(15,19)(16,22)(17,25)(26,29)(32,38)(35,42)(39,44)(43,45);(14,15,20,19)(16,23,22,18)(17,21,25,27)(24,29,28,26)(30,31,34,37)(32,35,38,42)(33,40,41,36)(39,45,44,43);(14,16)(15,18)(17,24)(19,23)(20,22)(21,26)(25,28)(27,29)(30,32)(31,35)(33,39)(34,38)(36,43)(37,42)(40,45)(41,44);(14,17)(15,21)(16,24)(18,26)(19,27)(20,25)(22,28)(23,29);(14,18,20,23)(15,22,19,16)(17,26,25,29)(21,28,27,24)(30,33,34,41)(31,36,37,40)(32,39,38,44)(35,43,42,45);(14,19,20,15)(16,23,22,18)(17,27,25,21)(24,29,28,26)(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, 55826);