Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#14584115 |
| Fitting, socle | C3×C72×C19 ⋊ C3 |
| derived, Hall | C72×C19 ⋊ C32 |
| Sylow | C72 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14584115 |
| commutator, hypocenter | C72×C19 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
939 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19150284, C3×#19150286, C3×#19150294, … |
| maximal normal subgroup of | C3×#19150284, C3×#19150286, C3×#19150294, … |
| maximal quotient of | C2×C3×#14584115, A4×#14584115, C3×C22⋊#14584115 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 47);