Finite Group Databasebeta

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C32×C5×D43⋊C7 #41029136

order27090
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D43⋊C7
unambiguous semidirect product(C32×D43)⋊(C5×C7)
unambiguous semidirect product(C32×C5×D43)⋊C7

Splittings

Fitting, socle, HallC32×C5×C43 ⋊ C2×C7
derived, SylowC43 ⋊ C2×C32×C5×C7
HallC32×C5×C43⋊C7 ⋊ C2
HallC32×C5×D43 ⋊ C7
HallC32×C43⋊C7 ⋊ C2×C5
HallC5×C43⋊C7 ⋊ C2×C32
HallC32×D43 ⋊ C5×C7
HallC5×D43 ⋊ C32×C7
HallC32×C43 ⋊ C2×C5×C7
HallC43⋊C7 ⋊ C2×C32×C5
HallC5×C43 ⋊ C2×C32×C7
HallD43 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC32×C5D43⋊C7
commutator, cosocle, hypocenterC43C2×C32×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C43C2×C7
LCSG ▷ C43
UCSC1 ◁ C32×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1935

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27090, 77);