Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×C8×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2966 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C2×C4×C8×C61 | C2 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | #2966 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^601976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29571052, #29571054, #29571059, … |
| maximal normal subgroup of | #29571052, #29571054, #29571059, … |
| maximal quotient of | #29678241, #29678261, #29678336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13485);