Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C13 · Schur multiplier (H2) = C214 |
| direct product | C13×#63076 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C26 |
| commutator | C2 | C25×C4×C13 |
| Frattini, cosocle | C4 | C26×C13 |
| socle | C2×C13 | C25×C4 |
| prime radical | C2×C13×#585 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ 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)(14,15,18,23,19,22,29,35)(16,20,26,32,25,31,38,42)(17,21,28,34,27,33,39,43)(24,30,37,41,36,40,44,45);(14,16)(15,20)(17,24)(18,26)(19,25)(21,30)(22,31)(23,32)(27,36)(28,37)(29,38)(33,40)(34,41)(35,42)(39,44)(43,45);(14,17)(15,21)(16,24)(18,28)(19,27)(20,30)(22,33)(23,34)(25,36)(26,37)(29,39)(31,40)(32,41)(35,43)(38,44)(42,45);(17,27)(21,33)(24,36)(28,39)(30,40)(34,43)(37,44)(41,45);(16,25)(20,31)(24,36)(26,38)(30,40)(32,42)(37,44)(41,45);(15,22)(20,31)(21,33)(23,35)(30,40)(32,42)(34,43)(41,45)1690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56064);