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D21×(C31⋊C3)⋊C5 #34086200

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD21×(C31⋊C3)⋊C5
unambiguous semidirect productC3⋊(D7×(C31⋊C3)⋊C5)
unambiguous semidirect product(D21×C31⋊C3)⋊C5

Splittings

Fitting, socle, derivedC3×C7×C31 ⋊ C2×C3×C5
HallC3×C7×(C31⋊C3)⋊C5 ⋊ C2
HallD21×C31⋊C3 ⋊ C5
HallC3×C7×C31⋊C3 ⋊ C2×C5
HallC3×(C31⋊C3)⋊C5 ⋊ D7
HallC7×ΓL(1,𝔽32) ⋊ C3×D3
HallC3×C31⋊C3 ⋊ C5×D7
HallC7×C31 ⋊ C3×C5×D3
HallΓL(1,𝔽32) ⋊ C3×D21
SylowC31 ⋊ C3×C5×D21
SylowC7 ⋊ D3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C31C2×C3×C5
LCSG ▷ C3×C7×C31
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 651

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 105);