Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#117×C61 ⋊ C2 |
| Sylow | C61 ⋊ #3449 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C25 |
| Frattini | C22 | C24×D61 |
| Fitting | C2×#117×C61 | C2 |
| hypercenter | C2×#117 | D61 |
| hypocenter | C61 | #3449 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 | |
1556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|e^2=f,b^a=bf,c^a=cg,d^a=df,h^a=h^60,c^b=cf,h^c=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29571848, #29571851, #29586650, … |
| maximal normal subgroup of | #29571848, #29571851, #29586650, … |
| maximal quotient of | #29838585, #29838642, #29838781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17843);