Finite Group DatabasebetaFinite Group Databasebeta| order | 9232 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C577 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D577 |
| commutator, hypocenter | C577 | C16 |
| Fitting | C8×C577 | C2 |
| socle | C2×C577 | C8 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,577|a^2=b,b^2=c,c^2=d,e^a=e^5762320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D577, C2×#22604393, #32914603, … |
| maximal normal subgroup of | C16×D577, C2×#22604393, #32914603, … |
| maximal quotient of | #32914570, C2×#22604393 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9232, 15);