Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C72×#4294 |
| derived, Sylow | C19 ⋊ C72×C9 |
| Hall | C72×C19 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | C19⋊C3 |
| commutator, hypocenter | C19 | C72×C9 |
| Frattini | C3 | C72×C19⋊C3 |
| Fitting, socle | C3×C72×C19 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C72 | |
60 conjugacy classes of subgroups.
1323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#4294⋊C2, C7×#4294⋊D7, C7×D7×#4294, … |
| maximal normal subgroup of | C72×#4294⋊C2, C7×#4294⋊D7, C7×D7×#4294, … |
| maximal quotient of | C2×C72×#4294, C72×C22⋊#4294 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 16);