Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63058 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6404 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)(16,21)(17,20)(18,22)(19,24)(23,28)(25,26)(27,29)(30,31,35,33)(32,38,40,36)(34,41,42,37)(39,43,45,44);(14,15)(16,21)(17,25)(18,22)(19,24)(20,26)(23,27)(28,29)(30,32,35,40)(31,36,33,38)(34,39,42,45)(37,43,41,44);(14,16)(15,19)(17,23)(18,24)(20,27)(21,22)(25,28)(26,29)(30,33,35,31)(32,36,40,38)(34,41,42,37)(39,43,45,44);(14,17)(15,20)(16,23)(18,26)(19,27)(21,28)(22,25)(24,29)(30,34)(31,37)(32,39)(33,41)(35,42)(36,43)(38,44)(40,45);(14,16)(15,21)(17,23)(18,24)(19,22)(20,28)(25,27)(26,29);(14,15)(16,19)(17,20)(18,22)(21,24)(23,27)(25,26)(28,29)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56046);