Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×#6923 |
| Fitting | H(5,𝔽2)×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#6923 |
| commutator, socle | C2×C61 | C24×C4 |
| Fitting | H(5,𝔽2)×C61 | C4 |
| hypercenter | H(5,𝔽2) | #6923 |
| hypocenter | C61 | C4×H(5,𝔽2) |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
1660 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
323 conjugacy classes — view the full character table.
| maximal subgroup of | #453×#6923, #455×#6923, #30616907, … |
| maximal normal subgroup of | #453×#6923, #455×#6923, #30616907, … |
| maximal quotient of | #518×#6923, #520×#6923, #534×#6923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21491);