Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×D4×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2993 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C8×D4×C61 | C2 |
| hypercenter | C8×D4 | D61 |
| hypocenter | C61 | #2993 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C8×D4 | |
354 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^60,c^b=ce,d^b=dg,h^c=h^60,h^d=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29650066, #29650070, #29650081, … |
| maximal normal subgroup of | #29650066, #29650070, #29650081, … |
| maximal quotient of | #29678834, #29678872, #29678974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13660);