Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#14584108 |
| Fitting | C3×C19×C49 ⋊ C3 |
| derived, Hall | C19×C49 ⋊ C32 |
| Sylow | C49 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14584108 |
| commutator, hypocenter | C19×C49 | C32 |
| Frattini | C7 | C3×#87705 |
| Fitting | C3×C19×C49 | C3 |
| socle | C3×C7×C19 | ΓL(1,𝔽8) |
| LCS | G ▷ C19×C49 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
939 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19150258, C3×#19150256, C3×#19150252, … |
| maximal normal subgroup of | C3×#19150258, C3×#19150256, C3×#19150252, … |
| maximal quotient of | C2×C3×#14584108, A4×#14584108, C3×C22⋊#14584108 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 13);