Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×D61⋊C8 |
| derived, Sylow | C61 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #6923 |
| commutator, hypocenter | C61 | C22×C4×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C42 | |
760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
608 conjugacy classes — view the full character table.
| maximal subgroup of | D61⋊#1273, #30595985, #30595989, … |
| maximal normal subgroup of | D61⋊#1273, #30595985, #30595989, … |
| maximal quotient of | C2×C8×D61⋊C8, C2×#21461013, M16×D61⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21060);