Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#14519702 |
| Sylow | C61 ⋊ C22×#103 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D244 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C23×C8×C61 | C2 |
| socle | C24×C61 | D4 |
| hypercenter | C23×C8 | D61 |
| hypocenter | C61 | C22×#103 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29585581, #29585585, #29586279, … |
| maximal normal subgroup of | #29585581, #29585585, #29586279, … |
| maximal quotient of | C22×#16839494, C2×#21444249, C2×#21444223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13001);