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C7×C3⋊(D67⋊C11) #44526249

order30954
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(D67⋊C11)
unambiguous semidirect productC3⋊(C7×D67⋊C11)
unambiguous semidirect productD201⋊(C7×C11)
unambiguous semidirect product(C67⋊C11)⋊(D3×C7)
unambiguous semidirect product(C7×D201)⋊C11

Splittings

Fitting, socle, HallC3×C7×C67 ⋊ C2×C11
derived, HallC3×C67 ⋊ C2×C7×C11
HallC3×C7×C67⋊C11 ⋊ C2
HallC7×C67⋊C11 ⋊ D3
HallC7×D201 ⋊ C11
HallC3×C67⋊C11 ⋊ C2×C7
HallC67⋊C11 ⋊ D3×C7
HallC7×C67 ⋊ D3×C11
HallD201 ⋊ C7×C11
SylowC67 ⋊ D3×C7×C11
HallC3×C7 ⋊ D67⋊C11
SylowC3 ⋊ C7×D67⋊C11

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(D67⋊C11)
commutator, cosocle, hypocenterC3×C67C2×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C67C2×C11
LCSG ▷ C3×C67
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1407

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 30);