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×#62941 |
| 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)(14,15,21,25)(16,26,29,22)(17,18,19,23)(20,27,28,24)(32,38)(36,40)(39,44)(43,45);(14,16,21,29)(15,22,25,26)(17,24,19,27)(18,28,23,20)(30,31,35,34)(32,36,38,40)(33,37,41,42)(39,43,44,45);(14,17,21,19)(15,23,25,18)(16,27,29,24)(20,22,28,26)(30,32)(31,36)(33,39)(34,40)(35,38)(37,43)(41,44)(42,45);(14,18)(15,17)(16,28)(19,25)(20,29)(21,23)(22,24)(26,27)(30,33)(31,37)(32,39)(34,42)(35,41)(36,43)(38,44)(40,45);(14,19,21,17)(15,23,25,18)(16,27,29,24)(20,26,28,22)(30,34,35,31)(32,40,38,36)(33,37,41,42)(39,43,44,45);(14,20,21,28)(15,24,25,27)(16,18,29,23)(17,22,19,26)(30,32)(31,36)(33,39)(34,40)(35,38)(37,43)(41,44)(42,45)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55929);