Finite Group DatabasebetaFinite Group Databasebeta| order | 12246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C157 ⋊ C2×C3 |
| Hall | #20259405 ⋊ C2 |
| Hall | C13×D157 ⋊ C3 |
| Hall | D157 ⋊ C13⋊C3 |
| Sylow | C157 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ D157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C157 | C2×C3 |
| LCS | G ▷ C13×C157 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,157|d^a=d^156,c^b=c^3,d^b=d^144352 conjugacy classes — view the full character table.
| maximal subgroup of | #37587607, #27133642⋊C2, #37587617, … |
| maximal normal subgroup of | #37587607, #27133642⋊C2, #37587617, … |
| maximal quotient of | #37587570, C2×#27133642, #49144998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12246, 21);