Finite Group Databasebeta

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C5×C7×(C43⋊C3)⋊C7 #44539178

order31605
automorphism?
homologyAbelianization (H1) = C3×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC5×C7×(C43⋊C3)⋊C7
unambiguous semidirect product(C43⋊C3)⋊(C5×C72)
unambiguous semidirect product(C43⋊C7)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C43⋊C3)⋊C72
unambiguous semidirect product(C7×C43⋊C3)⋊(C5×C7)
unambiguous semidirect product(C5×C43⋊C7)⋊(C3×C7)
unambiguous semidirect product(C5×C7×C43⋊C3)⋊C7

Splittings

Fitting, socleC5×C7×C43 ⋊ C3×C7
derived, SylowC43 ⋊ C3×C5×C72
HallC5×C7×C43⋊C7 ⋊ C3
HallC7×C43⋊C7 ⋊ C3×C5
HallC5×C43⋊C3 ⋊ C72
HallC5×C43 ⋊ C3×C72
HallC43⋊C3 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC5×C7(C43⋊C3)⋊C7
commutator, cosocle, hypocenterC43C3×C5×C72
FrattiniC1G
Fitting, socleC5×C7×C43C3×C7
LCSG ▷ C43
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1505

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31605, 9);