Finite Group Databasebeta

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C2×C3×(D127⋊C3)⋊C7 #44544776

order32004
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×(D127⋊C3)⋊C7
unambiguous semidirect product(D127⋊C3)⋊(C2×C3×C7)
unambiguous semidirect product(C2×D127⋊C3)⋊(C3×C7)
unambiguous semidirect product(D127⋊C7)⋊(C2×C32)
unambiguous semidirect product((C127⋊C3)⋊C7)⋊(C22×C3)
unambiguous semidirect product(C2×D127⋊C7)⋊C32
unambiguous semidirect product(C2×C3×D127⋊C3)⋊C7
unambiguous semidirect product(C2×(C127⋊C3)⋊C7)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D127⋊C7)⋊C3

Splittings

Fitting, socleC2×C3×C127 ⋊ C2×C3×C7
derived, SylowC127 ⋊ C22×C32×C7
HallC3×(C127⋊C3)⋊C7 ⋊ C22
HallC2×C3×D127⋊C3 ⋊ C7
HallC2×D127⋊C7 ⋊ C32
HallC3×C127⋊C3 ⋊ C22×C7
HallC127⋊C7 ⋊ C22×C32
HallC2×D127 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3(D127⋊C3)⋊C7
commutator, cosocle, hypocenterC127C22×C32×C7
FrattiniC1G
Fitting, socleC2×C3×C127C2×C3×C7
LCSG ▷ C127
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 762

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 158);