Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#226 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C41 | S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C2×C41 |
| Frattini | C2 | S4×C41 |
| Fitting | Q8×C41 | D3 |
| prime radical | SL(2,𝔽3)×C41 | C2 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C41 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 656 |
A minimal faithful permutation representation — 2 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(42,47,51,54,46,56,53,48)(43,52,55,45,49,44,57,50);(44,50,53)(45,51,52)(47,54,57)(48,55,56)328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 98);