Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C19⋊C3×#3862 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C32 |
| Sylow | C72 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 34);