Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#408 ⋊ C2 |
| Sylow | C61 ⋊ #2930 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C61×#408 | C2 |
| hypercenter | #408 | D61 |
| hypocenter | C61 | #2930 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #408 | |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^60,c^b=cg,h^b=h^60,h^c=h^60884 conjugacy classes — view the full character table.
| maximal subgroup of | #29589516, #29595169, #29595171, … |
| maximal normal subgroup of | #29589516, #29595169, #29595171, … |
| maximal quotient of | #29650208, #29650217, #29650226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13216);