Finite Group Databasebeta

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D7×C3⋊(C5⋊(D19⋊C3)) #37561354

order23940
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD7×C3⋊(C5⋊(D19⋊C3))
unambiguous semidirect product(D7×C19⋊C3)⋊D15

Splittings

Fitting, socle, derivedC3×C5×C7×C19 ⋊ C22×C3
HallC3×C5×C7×C19⋊C3 ⋊ C22
HallC3×C7×C19⋊C3 ⋊ C2×D5
HallC3×C5×C19⋊C3 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×C3×D3
HallC3×C19⋊C3 ⋊ D5×D7
HallC7×C19 ⋊ C2×C3×D15
HallC5×C19 ⋊ C3×D3×D7
HallC5×C7 ⋊ C2×C3⋊(D19⋊C3)
SylowC19 ⋊ C3×D7×D15
SylowC7 ⋊ C2×C3⋊(C5⋊(D19⋊C3))
SylowC5 ⋊ D7×C3⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C19C22×C3
LCSG ▷ C3×C5×C7×C19
UCSC1

176 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 1995

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 486);