Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | #67042⋊C5 |
| Fitting | C11×#41 ⋊ C2×C5 |
| Hall | #67042 ⋊ C5 |
| Hall | C11⋊C5 ⋊ H(5,𝔽2) |
| Sylow | C11 ⋊ C5×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×AGL(1,𝔽11) |
| commutator, socle, cosocle | C2×C11 | C24×C5 |
| Fitting | C11×#41 | C2×C5 |
| hypercenter | #41 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×H(5,𝔽2) |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ #41 | |
332 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^4,5,2,11|d^2=f,d^a=df,g^a=g^10,c^b=cf,g^e=g^495 conjugacy classes — view the full character table.
| maximal subgroup of | H(5,𝔽2)×AGL(1,𝔽11), #72222328, #72222331, … |
| maximal normal subgroup of | H(5,𝔽2)×AGL(1,𝔽11), #72222328, #72222331, … |
| maximal quotient of | #72222629, #72222645, C2×#67042⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1097);