Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #3861⋊(C19⋊C3) |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C32 |
| Sylow | C72 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)2 |
| 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.
Polycyclic presentation:
3^2,7^2,19|c^a=c^2,e^a=e^7,c^b=c^2,d^b=d^2139 conjugacy classes — view the full character table.
| maximal subgroup of | #30660660, #64424⋊(C19⋊C3), #30660674, … |
| maximal normal subgroup of | #30660660, #64424⋊(C19⋊C3), #30660674, … |
| maximal quotient of | C2×#3861⋊(C19⋊C3), #45692504, #45692505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 38);