Finite Group Databasebeta

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D11×C3⋊(C5⋊D35) #37528701

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

Aliases

direct productD11×C3⋊(C5⋊D35)
unambiguous semidirect product(C3×D11)⋊(C5⋊D35)
unambiguous semidirect product(C5×D11)⋊D105
unambiguous semidirect product(C7×D11)⋊(C3⋊(C5⋊D5))

Splittings

Fitting, socle, derived, HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ D3×D11
HallC7×C11 ⋊ C2×C3⋊(C5⋊D5)
HallC3×C52 ⋊ D7×D11
HallC3×C11 ⋊ C2×C5⋊D35
SylowC52 ⋊ D11×D21
HallC3×C7 ⋊ D11×C5⋊D5
SylowC11 ⋊ C2×C3⋊(C5⋊D35)
SylowC7 ⋊ D11×C3⋊(C5⋊D5)
SylowC3 ⋊ D11×C5⋊D35

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7×C11
UCSC1

320 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 512);