Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #63091 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C214 |
| direct product | C13×#63092 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C24×D4 |
| commutator, Frattini, cosocle | C4 | C26×C13 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C13×#585 ◁ G | |
10796 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,24)(16,21,26,34)(17,22,28,36)(18,20,30,23)(25,33,38,43)(27,31,40,35)(29,32,41,37)(39,42,45,44);(15,20)(18,30)(21,31)(22,32)(23,24)(27,40)(29,41)(33,42)(34,35)(36,37)(39,45)(43,44);(14,16)(15,21)(17,25)(18,27)(19,26)(20,31)(22,33)(23,35)(24,34)(28,38)(29,39)(30,40)(32,42)(36,43)(37,44)(41,45);(14,17)(15,22)(16,25)(18,29)(19,28)(20,32)(21,33)(23,37)(24,36)(26,38)(27,39)(30,41)(31,42)(34,43)(35,44)(40,45);(17,28)(22,36)(25,38)(29,41)(32,37)(33,43)(39,45)(42,44);(16,26)(21,34)(25,38)(27,40)(31,35)(33,43)(39,45)(42,44)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56080);