Finite Group DatabasebetaFinite Group Databasebeta| order | 5526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14583774⋊C2 |
| Fitting, socle, derived, Sylow | C307 ⋊ C2×C9 |
| Hall | #14583774 ⋊ C2 |
| Hall | D307 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C307 | C2×C9 |
| LCS | G ▷ C307 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,307|b^3=c,d^a=d^306,d^b=d^46,d^c=d^1735 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14583774⋊C2, C5×#14583774⋊C2, C5⋊(#14583774⋊C2) |
| maximal normal subgroup of | C2×#14583774⋊C2, C5×#14583774⋊C2 |
| maximal quotient of | #14583774⋊C4, C2×#14583774⋊C2, C5×#14583774⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5526, 8);