Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×C19⋊#3862 |
| unambiguous semidirect product | (C3×C19)⋊#3862 |
| Fitting, socle | C3×C72×C19 ⋊ C3 |
| derived, Hall | C72×C19 ⋊ C32 |
| Sylow | C72 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊#3862 |
| commutator, hypocenter | C72×C19 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
939 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19150290, C3×#19150291, C3×#19150300, … |
| maximal normal subgroup of | C3×#19150290, C3×#19150291, C3×#19150300, … |
| maximal quotient of | C2×C3×C19⋊#3862, A4×C19⋊#3862, C3×C22⋊(C19⋊#3862) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 41);