Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C61×#423 ⋊ C2 |
| Sylow | C61 ⋊ #1861 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14519745 |
| commutator | C2×C4×C61 | C22×C4 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#423 | C2 |
| socle | C2×C61 | #385 |
| hypercenter | #423 | D61 |
| hypocenter | C61 | #1861 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #423 | |
262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=f,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^b=h^60,e^c=eg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1861, C2×#21446058, #29680914, … |
| maximal normal subgroup of | D61×#1861, C2×#21446058, #29680914, … |
| maximal quotient of | #29573895, #29573902, #29573909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4749);