Finite Group Databasebeta

← Prev (#37528500) Next (#37528502) →

D11×(C5⋊D5)⋊ΓL(1,𝔽8) #37528501

order23100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productD11×(C5⋊D5)⋊ΓL(1,𝔽8)
unambiguous semidirect product(D11×C5⋊D5)⋊ΓL(1,𝔽8)

Splittings

Fitting, socle, derived, HallC52×C7×C11 ⋊ C22×C3
HallC7×D11×C5⋊D5 ⋊ C3
HallC11×C7⋊(C52⋊C3) ⋊ C22
HallD11×C5⋊D5 ⋊ ΓL(1,𝔽8)
HallC7⋊(C52⋊C3) ⋊ C2×D11
HallC52×C11 ⋊ C22×ΓL(1,𝔽8)
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×(C5⋊D5)⋊C3
SylowC52 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×(C5⋊D5)⋊ΓL(1,𝔽8)
SylowC7 ⋊ D11×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C11C22×C3
LCSG ▷ C52×C7×C11
UCSC1

120 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 27 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 312);