Finite Group DatabasebetaFinite Group Databasebeta| order | 11613 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×C49⋊C3 |
| unambiguous semidirect product | C49⋊(C3×C79) |
| Fitting, Hall | C49×C79 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C3×C79 |
| Frattini | C7 | ΓL(1,𝔽8)×C79 |
| Fitting | C49×C79 | C3 |
| socle | C7×C79 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C79 | |
12 conjugacy classes of subgroups.
1501 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C79×C49⋊C3, C49⋊C3×D79, C79×D49⋊C3, … |
| maximal normal subgroup of | C2×C79×C49⋊C3, C49⋊C3×D79, C79×D49⋊C3, … |
| maximal quotient of | C2×C79×C49⋊C3, C79×C49⋊C9, C3×C79×C49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11613, 2);