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C5×D3×C11×C43 #28381995

order14190
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C43 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C11×C43
unambiguous semidirect productC3⋊(C2×C5×C11×C43)

Splittings

Fitting, socle, HallC3×C5×C11×C43 ⋊ C2
derived, SylowC3 ⋊ C2×C5×C11×C43
HallC3×C11×C43 ⋊ C2×C5
HallC3×C5×C43 ⋊ C2×C11
HallC3×C5×C11 ⋊ C2×C43
HallC3×C43 ⋊ C2×C5×C11
HallC3×C11 ⋊ C2×C5×C43
HallC3×C5 ⋊ C2×C11×C43

Subgroups

subgroupG/H
center, hypercenterC5×C11×C43D3
commutator, cosocle, hypocenterC3C2×C5×C11×C43
FrattiniC1G
Fitting, socleC3×C5×C11×C43C2
LCSG ▷ C3
UCSC1 ◁ C5×C11×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7095

Conjugacy classes & character table

7095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D43, C5×D3×D11×C43, C5×D3×D473, …
maximal normal subgroup ofC5×D3×C11×D43, C5×D3×D11×C43, C5×D3×D473, …
maximal quotient ofC5×C11×Dic3×C43, C2×C5×D3×C11×C43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 12);