Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#493 ⋊ C2 |
| Sylow | C61 ⋊ #3287 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#493 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #493 | D61 |
| hypocenter | C61 | #3287 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^60,h^c=h^60,e^d=eg,h^d=h^60695 conjugacy classes — view the full character table.
| maximal subgroup of | #29593441, #29593445, #29593469, … |
| maximal normal subgroup of | #29593441, #29593445, #29593469, … |
| maximal quotient of | #29671039, #29671054, #29671069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 16268);