Finite Group DatabasebetaFinite Group Databasebeta| order | 1197 |
| isoclinism | isoclinic class of #87704 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#87704 |
| Fitting, socle | C3×C7×C19 ⋊ C3 |
| derived, Hall | C7×C19 ⋊ C32 |
| Sylow | C19 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #87704 |
| commutator, cosocle, hypocenter | C7×C19 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C19 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 399 |
141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11716327, C3×#11716325, C3×#11716321, … |
| maximal normal subgroup of | C3×#11716327, C3×#11716325, C3×#11716321, … |
| maximal quotient of | C2×C3×#87704, A4×#87704, C3×C22⋊#87704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1197, 13);