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×#62928 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6360 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)(16,22)(20,24)(23,28)(27,29)(30,31,34,37)(32,35,40,38)(33,41,42,36)(39,44,45,43);(14,15,19,18)(16,20,22,24)(17,21,25,26)(23,27,28,29)(30,31)(32,38)(33,36)(34,37)(35,40)(39,44)(41,42)(43,45);(14,16)(15,20)(17,23)(18,24)(19,22)(21,27)(25,28)(26,29)(30,32)(31,35)(33,39)(34,40)(36,43)(37,38)(41,44)(42,45);(14,17)(15,21)(16,23)(18,26)(19,25)(20,27)(22,28)(24,29)(30,33,34,42)(31,36,37,41)(32,39,40,45)(35,43,38,44);(14,18,19,15)(16,24,22,20)(17,21,25,26)(23,27,28,29);(14,16)(15,20)(17,23)(18,24)(19,22)(21,27)(25,28)(26,29)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55916);