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C3⋊(((C11⋊D11)⋊C3)⋊C5) #24926137

order10890
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(((C11⋊D11)⋊C3)⋊C5)
unambiguous semidirect product(C3⋊((C11⋊D11)⋊C3))⋊C5
unambiguous semidirect product(C3⋊#11925892)⋊C3

Splittings

Fitting, socle, derivedC3×C112 ⋊ C2×C3×C5
HallC3×(C112⋊C3)⋊C5 ⋊ C2
HallC3⋊((C11⋊D11)⋊C3) ⋊ C5
HallC3×C112⋊C3 ⋊ C2×C5
Hall#10597243 ⋊ C3×D3
SylowC112 ⋊ C3×C5×D3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C112C2×C3×C5
LCSG ▷ C3×C112
UCSC1

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,3,11^2|d^a=d^2,e^a=e^10,f^a=f^10,e^b=e^3f^9,f^b=ef^7,e^c=e^3,f^c=f^3

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#10624391⋊C5)⋊D3, D3×((C11⋊D11)⋊C3)⋊C5, C2×C3⋊(((C11⋊D11)⋊C3)⋊C5)
maximal normal subgroup of(#10624391⋊C5)⋊D3, D3×((C11⋊D11)⋊C3)⋊C5, C2×C3⋊(((C11⋊D11)⋊C3)⋊C5)
maximal quotient ofC3⋊(((C11⋊Dic11)⋊C3)⋊C5), C2×C3⋊(((C11⋊D11)⋊C3)⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 86);