Finite Group Databasebeta

← Prev (#44568652) Next (#44568654) →

C11×ΓL(1,𝔽8)⋊(C7⋊AGL(1,𝔽5)) #44568653

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C3×C4
derived, HallC5×C72 ⋊ C3×C4×C11
HallC11×C7⋊(C7⋊AGL(1,𝔽5)) ⋊ C3
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C4
HallC7×C11×ΓL(1,𝔽8) ⋊ AGL(1,𝔽5)
HallC7⋊(C7⋊AGL(1,𝔽5)) ⋊ C3×C11
HallC5×C7×ΓL(1,𝔽8) ⋊ C4×C11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
HallC7×ΓL(1,𝔽8) ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ ΓL(1,𝔽8)⋊Dic7
SylowC72 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×ΓL(1,𝔽8)⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalC7×D5×C11×ΓL(1,𝔽8)C2
cosocleC72×D5C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C11

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

869 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 355);