Finite Group DatabasebetaFinite Group Databasebeta| order | 9376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C293 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11924078 |
| commutator, socle | C2×C293 | C22×C4 |
| Fitting | Q8×C293 | C4 |
| hypercenter | Q8 | #11924078 |
| hypocenter | C293 | #131 |
| LCS | G ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,293|a^2=d,d^2=e,f^a=f^138,c^b=ce,f^b=f^292,f^c=f^292,f^d=f^292385 conjugacy classes — view the full character table.
| maximal subgroup of | #34037172, #34037173, #34037174, … |
| maximal normal subgroup of | #34037172, #34037173, #34037174, … |
| maximal quotient of | #34037094, #34037104, #34037136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9376, 234);