Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | #95×C61 | C4 |
| hypercenter | #95 | #6923 |
| hypocenter | C61 | #1840 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #95 | |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^11,c^b=cg,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21461748, D61⋊#1840, #30615285, … |
| maximal normal subgroup of | C2×#21461748, D61⋊#1840, #30615285, … |
| maximal quotient of | #30599488, #30599489, #30602611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20439);