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C7×C11×D123 #34038819

order18942
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D123
unambiguous semidirect productC3⋊(C7×C11×D41)
unambiguous semidirect productC41⋊(D3×C7×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C41 ⋊ C2
derived, HallC3×C41 ⋊ C2×C7×C11
HallC7×C11×C41 ⋊ D3
HallC3×C11×C41 ⋊ C2×C7
HallC3×C7×C41 ⋊ C2×C11
HallC11×C41 ⋊ D3×C7
HallC7×C41 ⋊ D3×C11
HallC3×C7×C11 ⋊ D41
SylowC41 ⋊ D3×C7×C11
HallC3×C11 ⋊ C7×D41
HallC3×C7 ⋊ C11×D41
SylowC3 ⋊ C7×C11×D41

Subgroups

subgroupG/H
center, hypercenterC7×C11D123
commutator, cosocle, hypocenterC3×C41C2×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C41C2
LCSG ▷ C3×C41
UCSC1 ◁ C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9471

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×C11×D41, C7×D11×D123, C7×D33⋊D41, …
maximal normal subgroup ofD3×C7×C11×D41, C7×D11×D123, C7×D33⋊D41, …
maximal quotient ofC7×C11×Dic123, C2×C7×C11×D123

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18942, 11);