Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#16840821 |
| Sylow | C61 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C4 | C23×#6923 |
| Fitting | C2×M16×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C2×M16 | #6923 |
| hypocenter | C61 | C2×#504 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
368 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #30606460, #30606461, #30606465, … |
| maximal normal subgroup of | #30606460, #30606461, #30606465, … |
| maximal quotient of | C2×#21462029, C2×#21462030, C4×#16840821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21476);