Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | C61×#376 | C2 |
| hypercenter | #376 | D61 |
| hypocenter | C61 | #1840 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^60,c^b=cg1244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#1840, C2×#21445964, #29680264, … |
| maximal normal subgroup of | D61×#1840, C2×#21445964, #29680264, … |
| maximal quotient of | #29573741, #29585622, #29588461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4655);