Finite Group DatabasebetaFinite Group Databasebeta| order | 7312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C457 ⋊ C2 |
| Sylow | C457 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D1828 |
| commutator | C4×C457 | C22 |
| Frattini | C4 | C2×D457 |
| Fitting | C8×C457 | C2 |
| socle | C2×C457 | D4 |
| hypercenter | C8 | D457 |
| hypocenter | C457 | SD16 |
| LCS | G ▷ C4×C457 ▷ C2×C457 ▷ C457 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,457|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^456,c^b=cd,e^b=e^4561831 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D457, C2×#20300730, #28410573, … |
| maximal normal subgroup of | SD16×D457, C2×#20300730, #28410573, … |
| maximal quotient of | #28410474, #28410477, #28410484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7312, 29);