Finite Group Databasebeta

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D3×C7×C11×C5⋊D5 #37528706

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

Aliases

direct productD3×C7×C11×C5⋊D5
unambiguous semidirect product(C5×D3)⋊(C7×D5×C11)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C22
derived, HallC3×C52 ⋊ C22×C7×C11
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C22×C7
HallC3×C52×C7 ⋊ C22×C11
HallC52×C11 ⋊ C2×D3×C7
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×D3×C11
HallC3×C11 ⋊ C2×C7×C5⋊D5
SylowC52 ⋊ C2×D3×C7×C11
HallC3×C7 ⋊ C2×C11×C5⋊D5
SylowC3 ⋊ C2×C7×C11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC7×C11D3×C5⋊D5
commutator, cosocle, hypocenterC3×C52C22×C7×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52
UCSC1 ◁ C7×C11

320 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 112 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

3234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 517);