Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C61×#520 ⋊ C2 |
| Sylow | C61 ⋊ C4×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator | C2×C61 | C24×C4 |
| Fitting | C61×#520 | C2 |
| socle | C22×C61 | C25 |
| hypercenter | #520 | D61 |
| hypocenter | C61 | C4×2−1+4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=f,c^2=f,e^2=g,b^a=bf,d^a=df,c^b=cf,h^c=h^60,h^e=h^601088 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29685906, #29685912, #29685917, … |
| maximal normal subgroup of | #29685906, #29685912, #29685917, … |
| maximal quotient of | #29838251, #29838254, #520×Dic61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17721);