Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C61×#388 ⋊ C2 |
| Sylow | C61 ⋊ #2597 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C61×#388 | C2 |
| hypercenter | #388 | D61 |
| hypocenter | C61 | #2597 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #388 | |
454 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=eg,b^2=fg,c^2=g,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^60,c^b=cg,h^b=h^60,h^c=h^60878 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2597, C2×#21451376, #29850608, … |
| maximal normal subgroup of | D61×#2597, C2×#21451376, #29850608, … |
| maximal quotient of | #29602511, #29602622, #29603634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 10067);