Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4×D4×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2636 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C2×C4×D4×C61 | C2 |
| hypercenter | C2×C4×D4 | D61 |
| hypocenter | C61 | #2636 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
562 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^601232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29653433, #29653437, #29653463, … |
| maximal normal subgroup of | #29653433, #29653437, #29653463, … |
| maximal quotient of | #29606467, #29606497, #29606685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 10405);