Finite Group DatabasebetaFinite Group Databasebeta| order | 7408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D1852 |
| Fitting | C2×C4×C463 ⋊ C2 |
| Sylow | C463 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D463 |
| commutator | C2×C463 | C23 |
| Frattini | C2 | C22×D463 |
| Fitting | C2×C4×C463 | C2 |
| socle | C22×C463 | C22 |
| hypercenter | C2×C4 | D463 |
| hypocenter | C463 | C2×D4 |
| LCS | G ▷ C2×C463 ▷ C463 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
1858 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28414574, #28414578, #28414580, … |
| maximal normal subgroup of | #28414574, #28414578, #28414580, … |
| maximal quotient of | C2×(C2×D463)⋊C4, C2×C4⋊Dic463, C4×D1852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7408, 36);