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C7×C11×C22⋊(C52⋊C3) #37528730

order23100
automorphism?
homologyAbelianization (H1) = C3×C7×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC7×C11×C22⋊(C52⋊C3)
unambiguous semidirect productC22⋊(C7×C11×C52⋊C3)
unambiguous semidirect productC52⋊(C7×C11×A4)
unambiguous semidirect product(C22×C11)⋊(C7×C52⋊C3)
unambiguous semidirect product(C52×C11)⋊(C7×A4)

Splittings

Fitting, socle, HallC22×C52×C7×C11 ⋊ C3
derived, HallC22×C52 ⋊ C3×C7×C11
HallC52×C7×C11 ⋊ A4
HallC22×C52×C11 ⋊ C3×C7
HallC22×C52×C7 ⋊ C3×C11
HallC22×C7×C11 ⋊ C52⋊C3
HallC52×C11 ⋊ C7×A4
HallC52×C7 ⋊ C11×A4
HallC22×C11 ⋊ C7×C52⋊C3
HallC22×C7 ⋊ C11×C52⋊C3
SylowC52 ⋊ C7×C11×A4
SylowC22 ⋊ C7×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC7×C11C22⋊(C52⋊C3)
commutator, cosocle, hypocenterC22×C52C3×C7×C11
FrattiniC1G
Fitting, socleC22×C52×C7×C11C3
LCSG ▷ C22×C52
UCSC1 ◁ C7×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 541);