Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C233 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D233 |
| commutator, hypocenter | C233 | C32 |
| Fitting | C16×C233 | C2 |
| socle | C2×C233 | C16 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2321888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D233, C2×#21418441, #28416268, … |
| maximal normal subgroup of | C32×D233, C2×#21418441, #28416268, … |
| maximal quotient of | #28416154, C2×#21418441 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 52);