Finite Group DatabasebetaFinite Group Databasebeta| order | 16458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C211 ⋊ C2×C3 |
| Hall | #22551750 ⋊ C2 |
| Hall | C13×D211 ⋊ C3 |
| Hall | D211 ⋊ C13⋊C3 |
| Sylow | C211 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ D211⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C211 | C2×C3 |
| LCS | G ▷ C13×C211 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2743 |
Polycyclic presentation:
2,3,13,211|d^a=d^210,c^b=c^3,d^b=d^196469 conjugacy classes — view the full character table.
| maximal subgroup of | #30657971⋊C2, C2×#30657971 |
| maximal normal subgroup of | #30657971⋊C2, C2×#30657971 |
| maximal quotient of | #45681781, C2×#30657971 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16458, 15);