Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C61 ⋊ Q128 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16839597 |
| commutator | C32×C61 | C22 |
| Frattini | C32 | C2×D61 |
| Fitting | C61×Q64 | C2 |
| socle | C2×C61 | D32 |
| hypercenter | Q64 | D61 |
| hypocenter | C61 | Q128 |
| LCS | G ▷ C32×C61 ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ Q64 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^60605 conjugacy classes — view the full character table.
| maximal subgroup of | D61×Q128, C2×#21444036, #29601065, … |
| maximal normal subgroup of | D61×Q128, C2×#21444036, #29601065, … |
| maximal quotient of | #29567893, #29567894, #29567912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2727);