Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C29×Q128 ⋊ C2 |
| Sylow | C29 ⋊ SD256 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16817704 |
| commutator | C29×C64 | C22 |
| Frattini | C64 | C2×D29 |
| Fitting | C29×Q128 | C2 |
| socle | C2×C29 | D64 |
| hypercenter | Q128 | D29 |
| hypocenter | C29 | SD256 |
| LCS | G ▷ C29×C64 ▷ C29×C32 ▷ C16×C29 ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ C64 ◁ Q128 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,29|a^2=h,c^2=de,d^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,g^a=gh,c^b=cd,d^b=de,e^b=ef,f^b=fg,g^b=gh,i^b=i^28557 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 57482);