Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#11924777 |
| derived | C7×C19 ⋊ C7×C9 |
| Hall | C72×C19 ⋊ C9 |
| Sylow | C72 ⋊ #4294 |
| Sylow | C19 ⋊ C7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #87705 |
| commutator, hypocenter | C7×C19 | C7×C9 |
| Frattini | C3 | C7×#87705 |
| Fitting, socle | C3×C72×C19 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3×C7 | |
32 conjugacy classes of subgroups.
987 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14558787, C7×#14558785, C7×#14558781, … |
| maximal normal subgroup of | C7×#14558787, C7×#14558785, C7×#14558781, … |
| maximal quotient of | C2×C7×#11924777, C7×C22⋊#11924777 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 19);