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C2×C7×C11×(C5⋊D5)⋊C3 #37528579

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C11 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derived, SylowC52 ⋊ C22×C3×C7×C11
HallC2×C7×C11×C5⋊D5 ⋊ C3
HallC7×C11×C52⋊C3 ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC2×C11×C5⋊D5 ⋊ C3×C7
HallC11×C52⋊C3 ⋊ C22×C7
HallC2×C7×C5⋊D5 ⋊ C3×C11
HallC7×C52⋊C3 ⋊ C22×C11
HallC52×C11 ⋊ C22×C3×C7
HallC52×C7 ⋊ C22×C3×C11
HallC2×C5⋊D5 ⋊ C3×C7×C11
HallC52⋊C3 ⋊ C22×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C22×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C7×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 390);