Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C61×#322 ⋊ C2 |
| Sylow | C61 ⋊ #1450 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D61 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | C61×#322 | C2 |
| socle | C22×C61 | C2×C42 |
| hypercenter | #322 | D61 |
| hypocenter | C61 | #1450 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ #322 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,b^2=e,d^2=f,e^2=g,h^a=h^60,c^b=cf,h^c=h^601280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29589016, #29589020, #29589067, … |
| maximal normal subgroup of | #29589016, #29589020, #29589067, … |
| maximal quotient of | #29569371, #29569397, #29570441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2795);