Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#408 ⋊ C2 |
| Sylow | C61 ⋊ #2978 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C61×#408 | C2 |
| hypercenter | #408 | D61 |
| hypocenter | C61 | #2978 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #408 | |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ceg,d^b=dg,h^c=h^60878 conjugacy classes — view the full character table.
| maximal subgroup of | #29596798, #29596800, #29596802, … |
| maximal normal subgroup of | #29596798, #29596800, #29596802, … |
| maximal quotient of | #29678717, #29678737, #29678796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13568);