Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C131 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C7×C131 ⋊ C3 |
| derived, Hall | C22×C7 ⋊ C3×C131 |
| Hall | C7×C131 ⋊ A4 |
| Hall | C22×C131 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ A4×C131 |
| Sylow | C22 ⋊ ΓL(1,𝔽8)×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | C22⋊ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×C7 | C3×C131 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C131 | C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C131 | |
20 conjugacy classes of subgroups.
1572 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×ΓL(1,𝔽8)×C131, C3×C22⋊ΓL(1,𝔽8)×C131 |
| maximal normal subgroup of | A4×ΓL(1,𝔽8)×C131, C3×C22⋊ΓL(1,𝔽8)×C131 |
| maximal quotient of | C131×C22⋊(C7⋊C9), C3×C22⋊ΓL(1,𝔽8)×C131 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 25);