Finite Group DatabasebetaFinite Group Databasebeta| order | 9392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic587 |
| Sylow | C587 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D587 |
| commutator | C2×C587 | C2×C4 |
| Fitting | C2×C4×C587 | C2 |
| socle | C22×C587 | C22 |
| hypercenter | C2×C4 | D587 |
| hypocenter | C587 | C4⋊C4 |
| LCS | G ▷ C2×C587 ▷ C587 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,587|a^2=d,b^2=c,b^a=bc,e^a=e^5862354 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34037542, #34037543, #34037545, … |
| maximal normal subgroup of | #34037542, #34037543, #34037545, … |
| maximal quotient of | C587⋊#95, C4⋊(C587⋊C8), #34037553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9392, 20);