Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2321 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C22×C22⋊C4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C22×C22⋊C4 | D61 |
| hypocenter | C61 | #2321 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
808 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^60,c^b=ce1244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29575545, #29575555, #29686014, … |
| maximal normal subgroup of | #29575545, #29575555, #29686014, … |
| maximal quotient of | #29601254, #29601296, #29601314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 7168);