Finite Group Databasebeta

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C2×C5×C7×D43⋊C3 #31825458

order18060
isoclinismisoclinic class of D43⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D43⋊C3

Splittings

Fitting, socleC2×C5×C7×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C22×C3×C5×C7
HallC2×C5×C7×D43 ⋊ C3
HallC5×C7×C43⋊C3 ⋊ C22
HallC5×C7×C43 ⋊ C22×C3
HallC2×C7×D43 ⋊ C3×C5
HallC7×C43⋊C3 ⋊ C22×C5
HallC2×C5×D43 ⋊ C3×C7
HallC5×C43⋊C3 ⋊ C22×C7
HallC7×C43 ⋊ C22×C3×C5
HallC5×C43 ⋊ C22×C3×C7
HallC2×D43 ⋊ C3×C5×C7
HallC43⋊C3 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D43⋊C3
commutator, cosocle, hypocenterC43C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3010

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 134);