Finite Group Databasebeta

← Prev (#37528575) Next (#37528577) →

C2×D11×C7⋊(C52⋊C3) #37528576

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

Aliases

direct productC2×D11×C7⋊(C52⋊C3)
unambiguous semidirect productC11⋊(C22×C7⋊(C52⋊C3))
unambiguous semidirect product(C2×C11)⋊(C2×C7⋊(C52⋊C3))
unambiguous semidirect product(C2×C7×D11)⋊(C52⋊C3)
unambiguous semidirect product(C2×C52×D11)⋊ΓL(1,𝔽8)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derived, HallC52×C7×C11 ⋊ C22×C3
HallC2×C52×C7×D11 ⋊ C3
HallC11×C7⋊(C52⋊C3) ⋊ C22
HallC2×C52×D11 ⋊ ΓL(1,𝔽8)
HallC2×C7×D11 ⋊ C52⋊C3
HallC52×C11 ⋊ C22×ΓL(1,𝔽8)
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C22×C52⋊C3
SylowC52 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C22×C7⋊(C52⋊C3)
SylowC7 ⋊ C2×D11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D11×C7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7×C11C22×C3
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2×C3
LCSG ▷ C52×C7×C11
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 387);