Finite Group DatabasebetaFinite Group Databasebeta| order | 9364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2341 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2341 | C4 |
| LCS | G ▷ C2341 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,2341|a^2=b,c^a=c^153,c^b=c^2340589 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22627296, #22627296⋊C3, C3×#22627296, … |
| maximal normal subgroup of | C2×#22627296, #22627296⋊C3, C3×#22627296 |
| maximal quotient of | #34035406, C2×#22627296, C3×#22627296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9364, 3);