Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C61×#557 ⋊ C2 |
| Sylow | C61 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×#557 | C2 |
| hypercenter | #557 | D61 |
| hypocenter | C61 | Q8×#41 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1068 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^60,h^d=h^60,h^e=h^60800 conjugacy classes — view the full character table.
| maximal subgroup of | #29655992, #29656000, #29656007, … |
| maximal normal subgroup of | #29655992, #29656000, #29656007, … |
| maximal quotient of | C4⋊C4×#11758226, #29839330, #29839440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 18092);