Finite Group DatabasebetaFinite Group Databasebeta| order | 7408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C463 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D463 |
| commutator | C4×C463 | C22 |
| Frattini | C4 | C2×D463 |
| Fitting | Q8×C463 | C2 |
| socle | C2×C463 | D4 |
| hypercenter | Q8 | D463 |
| hypocenter | C463 | Q16 |
| LCS | G ▷ C4×C463 ▷ C2×C463 ▷ C463 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,463|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^4621162 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q16×D463, C2×#20301780, #28414678, … |
| maximal normal subgroup of | Q16×D463, C2×#20301780, #28414678, … |
| maximal quotient of | #28414581, #28414582, #28414591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7408, 30);