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C2×C11⋊(D7⋊(C52⋊C3)) #37528575

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

Aliases

direct productC2×C11⋊(D7⋊(C52⋊C3))
unambiguous semidirect product(C2×C11)⋊(D7⋊(C52⋊C3))
unambiguous semidirect product(C2×D77)⋊(C52⋊C3)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derived, HallC52×C7×C11 ⋊ C22×C3
HallC2×C52×D77 ⋊ C3
HallC11×C7⋊(C52⋊C3) ⋊ C22
HallC7⋊(C52⋊C3) ⋊ C2×D11
HallC2×D77 ⋊ C52⋊C3
HallC52×C11 ⋊ C2×AGL(1,𝔽7)
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C22×C52⋊C3
SylowC52 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C2×D7⋊(C52⋊C3)
SylowC7 ⋊ C2×D11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊(D7⋊(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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 386);