Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#413 ⋊ C2 |
| Sylow | C61 ⋊ #3067 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14519750 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#413 | C2 |
| socle | C2×C61 | C2×#121 |
| hypercenter | #413 | D61 |
| hypocenter | C61 | #3067 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #413 | |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^60,f^c=fg,h^c=h^60692 conjugacy classes — view the full character table.
| maximal subgroup of | #29686950, #29686951, #29686961, … |
| maximal normal subgroup of | #29686950, #29686951, #29686961, … |
| maximal quotient of | #29662254, #29662282, #29662322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 14229);