Finite Group Databasebeta

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C7×C11×D111 #30685306

order17094
isoclinismisoclinic class of D111
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D111
unambiguous semidirect productC3⋊(C7×C11×D37)
unambiguous semidirect productC37⋊(D3×C7×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C2
derived, HallC3×C37 ⋊ C2×C7×C11
HallC7×C11×C37 ⋊ D3
HallC3×C11×C37 ⋊ C2×C7
HallC3×C7×C37 ⋊ C2×C11
HallC11×C37 ⋊ D3×C7
HallC7×C37 ⋊ D3×C11
HallC3×C7×C11 ⋊ D37
SylowC37 ⋊ D3×C7×C11
HallC3×C11 ⋊ C7×D37
HallC3×C7 ⋊ C11×D37
SylowC3 ⋊ C7×C11×D37

Subgroups

subgroupG/H
center, hypercenterC7×C11D111
commutator, cosocle, hypocenterC3×C37C2×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C37C2
LCSG ▷ C3×C37
UCSC1 ◁ C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

4389 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×C11×D37, C7×D11×D111, C7×D33⋊D37, …
maximal normal subgroup ofD3×C7×C11×D37, C7×D11×D111, C7×D33⋊D37, …
maximal quotient ofC7×C11×Dic111, C2×C7×C11×D111

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17094, 14);