Finite Group Databasebeta

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C2×C7×C11⋊((C5⋊D5)⋊C3) #37528580

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C7×C11⋊((C5⋊D5)⋊C3)
unambiguous semidirect product(C2×C11)⋊(C7×(C5⋊D5)⋊C3)
unambiguous semidirect product(C2×C5⋊D55)⋊(C3×C7)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derived, HallC52×C11 ⋊ C22×C3×C7
HallC2×C7×C5⋊D55 ⋊ C3
HallC7×C11×C52⋊C3 ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC2×C5⋊D55 ⋊ C3×C7
HallC11×C52⋊C3 ⋊ C22×C7
HallC7×C52⋊C3 ⋊ C2×D11
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×(C5⋊D5)⋊C3
HallC52⋊C3 ⋊ C2×C7×D11
SylowC52 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C7×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7C11⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C11C22×C3×C7
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2×C3
LCSG ▷ C52×C11
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 391);