Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C72×#4296 |
| Fitting, socle, Hall | C72×C19 ⋊ C9 |
| derived, Sylow | C19 ⋊ C72×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | #4296 |
| commutator, hypocenter | C19 | C72×C9 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C72 | |
60 conjugacy classes of subgroups.
539 conjugacy classes — view the full character table.
| maximal subgroup of | C72×AGL(1,𝔽19), C7×#4296⋊D7, C7×D7×#4296, … |
| maximal normal subgroup of | C72×AGL(1,𝔽19), C7×#4296⋊D7, C7×D7×#4296, … |
| maximal quotient of | C2×C72×#4296, C72×C22⋊#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 26);