Finite Group DatabasebetaFinite Group Databasebeta| order | 23226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C49×C79 ⋊ C2×C3 |
| Hall | #26042470 ⋊ C2 |
| Hall | C79×D49 ⋊ C3 |
| Hall | D49 ⋊ C79⋊C3 |
| Sylow | C79 ⋊ D49⋊C3 |
| Sylow | C49 ⋊ C2×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C79 | C2×C3 |
| Frattini | C7 | #15693302 |
| socle | C7×C79 | AGL(1,𝔽7) |
| LCS | G ▷ C49×C79 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3871 |
Polycyclic presentation:
2,3,7,79,7|c^7=e^6,c^a=c^6e,e^a=e^6,c^b=c^2e^3,d^b=d^23,e^b=e^2690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23226, 19);