Finite Group Databasebeta

← Prev (#17986927) Next (#17986929) →

C3⋊D759 #17986928

order4554
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊D759
unambiguous semidirect productC11⋊(C3⋊D69)
unambiguous semidirect productC23⋊(C3⋊D33)

Splittings

Fitting, socle, derived, HallC32×C11×C23 ⋊ C2
HallC11×C23 ⋊ C3⋊D3
HallC32×C23 ⋊ D11
HallC32×C11 ⋊ D23
SylowC23 ⋊ C3⋊D33
SylowC11 ⋊ C3⋊D69
SylowC32 ⋊ D253

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C23C2
LCSG ▷ C32×C11×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2277

Polycyclic presentation:

2,3^2,11,23|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^22

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3⋊(C3⋊(C23⋊AGL(1,𝔽11))), C5×C3⋊D759, C3⋊D3795, …
maximal normal subgroup ofC3⋊(C3⋊(C23⋊AGL(1,𝔽11))), C5×C3⋊D759, C7×C3⋊D759
maximal quotient ofC5×C3⋊D759, C3⋊D3795, C7×C3⋊D759, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 30);