Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C61×#529 ⋊ C2 |
| Sylow | C61 ⋊ #3444 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C25 |
| Frattini | C22 | C24×D61 |
| Fitting | C61×#529 | C2 |
| hypercenter | #529 | D61 |
| hypocenter | C61 | #3444 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #529 | |
1212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|d^2=g,e^2=f,b^a=bf,c^a=cg,h^c=h^60,h^e=h^60896 conjugacy classes — view the full character table.
| maximal subgroup of | #29646523, #29646546, #29646572, … |
| maximal normal subgroup of | #29646523, #29646546, #29646572, … |
| maximal quotient of | #29838313, #29838414, #29838416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17804);