Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62910 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6678 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)(16,23)(17,20)(18,21)(19,25)(22,27)(24,28)(26,29)(32,39)(36,43)(40,44)(41,45);(14,16,20,18)(15,21,17,23)(19,24,27,26)(22,28,25,29)(30,31,35,38)(32,36,39,43)(33,34,37,42)(40,41,44,45);(14,15,20,17)(16,23,18,21)(19,22,27,25)(24,29,26,28)(30,32)(31,36)(33,40)(34,41)(35,39)(37,44)(38,43)(42,45);(14,17,20,15)(16,23,18,21)(19,25,27,22)(24,29,26,28)(30,33)(31,34)(32,40)(35,37)(36,41)(38,42)(39,44)(43,45);(14,18,20,16)(15,21,17,23)(19,26,27,24)(22,28,25,29)(30,34)(31,37)(32,41)(33,38)(35,42)(36,44)(39,45)(40,43);(14,19)(15,22)(16,24)(17,25)(18,26)(20,27)(21,28)(23,29)(30,32)(31,36)(33,40)(34,41)(35,39)(37,44)(38,43)(42,45)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55898);