Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C19 ⋊ C9 |
| Sylow | C72 ⋊ #4294 |
| Sylow | C19 ⋊ #89204 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14584116 |
| commutator, hypocenter | C72×C19 | C9 |
| Fitting, socle | C3×C72×C19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
3,7^2,19,3|a^3=e,b^a=b^2,c^a=c^2,d^a=d^11939 conjugacy classes — view the full character table.
| maximal subgroup of | #30660573, #30660575, #30660583, … |
| maximal normal subgroup of | #30660573, #30660575, #30660583, … |
| maximal quotient of | C2×#22552710, C22⋊#22552710 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 22);