Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16836581 |
| Fitting | C2×Q8×C233 ⋊ C2 |
| Sylow | C233 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D233 |
| commutator | C4×C233 | C23 |
| Frattini | C4 | C22×D233 |
| Fitting | C2×Q8×C233 | C2 |
| socle | C22×C233 | D4 |
| hypercenter | C2×Q8 | D233 |
| hypocenter | C233 | C2×SD16 |
| LCS | G ▷ C4×C233 ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
1174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28416520, C4×#16836581, #28416533, … |
| maximal normal subgroup of | #28416520, C4×#16836581, #28416533, … |
| maximal quotient of | C2×#21418455, C2×#21418459, C2×#21418466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 159);