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×#62653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator | C2 | C25×C4×C13 |
| Frattini, cosocle | C22 | C26×C13 |
| prime radical | C22×C13×2−1+4 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
10930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,25)(21,26)(22,34)(23,24)(27,35)(28,38)(29,43)(30,36)(31,40)(32,46)(33,37)(39,44)(41,47)(42,49)(45,48);(19,24)(25,36)(26,37)(27,34)(38,40)(39,43)(41,46)(48,49);(18,20,23,30)(19,25,24,36)(21,31,33,28)(22,29,35,44)(26,40,37,38)(27,39,34,43)(32,45,47,42)(41,49,46,48);(18,21,23,33)(19,26,24,37)(20,28,30,31)(22,32,35,47)(25,38,36,40)(27,41,34,46)(29,42,44,45)(39,48,43,49);(18,19)(20,25)(21,26)(22,27)(23,24)(28,38)(29,39)(30,36)(31,40)(32,41)(33,37)(34,35)(42,48)(43,44)(45,49)(46,47);(18,22)(19,27)(20,29)(21,32)(23,35)(24,34)(25,39)(26,41)(28,42)(30,44)(31,45)(33,47)(36,43)(37,46)(38,48)(40,49)1690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55641);