Finite Group Databasebeta

← Prev (#37528533) Next (#37528535) →

C11×(C5⋊AGL(1,𝔽7))⋊D5 #37528534

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×(C5⋊AGL(1,𝔽7))⋊D5
unambiguous semidirect product(C5⋊AGL(1,𝔽7))⋊(D5×C11)
unambiguous semidirect product((C5⋊D5)⋊D7)⋊(C3×C11)
unambiguous semidirect product(C11×(C5⋊D5)⋊D7)⋊C3

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C22×C3
derived, HallC52×C7 ⋊ C22×C3×C11
HallC11×(C5⋊D5)⋊D7 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C22
Hall(C5⋊D5)⋊D7 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C22×C11
HallC52×C11 ⋊ C2×AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ D52
HallC7×C11 ⋊ C3×D52
SylowC52 ⋊ C2×C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D52×C11
SylowC7 ⋊ C3×D52×C11

Subgroups

subgroupG/H
center, hypercenterC11(C5⋊AGL(1,𝔽7))⋊D5
commutator, cosocle, hypocenterC52×C7C22×C3×C11
FrattiniC1G
Fitting, socleC52×C7×C11C22×C3
LCSG ▷ C52×C7
UCSC1 ◁ C11

192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 770

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 345);