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×#62949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6346 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(20,26)(21,27)(28,29)(30,31)(32,40)(33,34)(35,37)(36,39)(38,45)(41,42)(43,44);(30,32,36,35)(31,37,39,40)(33,43,38,41)(34,42,45,44);(14,15)(16,20)(17,21)(18,19)(22,28)(23,26)(24,29)(25,27)(30,33,36,38)(31,34,39,45)(32,41,35,43)(37,44,40,42);(14,16,18,23)(15,20,19,26)(17,24,25,22)(21,29,27,28)(30,34)(31,38)(32,42)(33,39)(35,44)(36,45)(37,41)(40,43);(14,17,18,25)(15,21,19,27)(16,22,23,24)(20,28,26,29)(30,35,36,32)(31,37,39,40)(33,43,38,41)(34,44,45,42);(14,15)(16,20)(17,21)(18,19)(22,28)(23,26)(24,29)(25,27)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55937);