Finite Group Databasebeta

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C5×D21×D19⋊C3 #37561313

order23940
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D21×D19⋊C3
unambiguous semidirect productD19⋊(C3×C5×D21)
unambiguous semidirect product(C3×D19⋊C3)⋊(C5×D7)
unambiguous semidirect product(C7×D19⋊C3)⋊(C5×D3)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C22×C3
derivedC3×C7×C19 ⋊ C22×C3×C5
HallC3×C5×C7×C19⋊C3 ⋊ C22
HallC3×C7×C19⋊C3 ⋊ C22×C5
HallC3×C5×C19⋊C3 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×C3×D3
HallC3×C19⋊C3 ⋊ C2×C5×D7
HallC7×C19 ⋊ C2×C3×C5×D3
HallC5×C19 ⋊ C2×C3×D21
HallC5×C7 ⋊ D3×D19⋊C3
SylowC19 ⋊ C2×C3×C5×D21
SylowC7 ⋊ C5×D3×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D21×D19⋊C3
commutator, cosocle, hypocenterC3×C7×C19C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22×C3
LCSG ▷ C3×C7×C19
UCSC1 ◁ C5

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 445);