Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×#117×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2471 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C2×#117×C61 | C2 |
| hypercenter | C2×#117 | D61 |
| hypocenter | C61 | #2471 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
582 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=ef,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^601238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#2471, C2×#21449924, #29848599, … |
| maximal normal subgroup of | D61×#2471, C2×#21449924, #29848599, … |
| maximal quotient of | #29602151, #29602592, #29602970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 8615);