Finite Group Databasebeta

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C3×C5×C7×C43⋊C7 #44539182

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

Aliases

direct productC3×C5×C7×C43⋊C7
unambiguous semidirect product(C3×C43)⋊(C5×C72)
unambiguous semidirect product(C3×C5×C43)⋊C72
unambiguous semidirect product(C3×C7×C43)⋊(C5×C7)
unambiguous semidirect product(C3×C5×C7×C43)⋊C7

Splittings

Fitting, socleC3×C5×C7×C43 ⋊ C7
derived, SylowC43 ⋊ C3×C5×C72
HallC3×C5×C43 ⋊ C72
HallC5×C43 ⋊ C3×C72
HallC3×C43 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C43⋊C7
commutator, cosocle, hypocenterC43C3×C5×C72
FrattiniC1G
Fitting, socleC3×C5×C7×C43C7
LCSG ▷ C43
UCSC1 ◁ C3×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4515

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31605, 13);