Finite Group DatabasebetaFinite Group Databasebeta| order | 23226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C79 ⋊ C2×C3 |
| Hall | #26042478 ⋊ C2 |
| Hall | C79×C7⋊D7 ⋊ C3 |
| Hall | C7⋊D7 ⋊ C79⋊C3 |
| Sylow | C79 ⋊ #64424 |
| Sylow | C72 ⋊ C2×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C79 | C2×C3 |
| LCS | G ▷ C72×C79 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3871 |
Polycyclic presentation:
2,3,7^2,79|c^a=c^6,d^a=d^6,c^b=c^2,d^b=d^2,e^b=e^23690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23226, 58);