Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #120×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2321 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | #120×C61 | C4 |
| hypercenter | #120 | #6923 |
| hypocenter | C61 | #2321 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #120 | |
808 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^50,c^b=ce,h^b=h^11,h^g=h^60254 conjugacy classes — view the full character table.
| maximal subgroup of | #30606516, #30616922, C2×#21462304, … |
| maximal normal subgroup of | #30606516, #30616922, C2×#21462304, … |
| maximal quotient of | #30608656, #30608673, #30608677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20995);