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C11⋊C5×(C43⋊C3)⋊C4 #43248787

order28380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×(C43⋊C3)⋊C4
unambiguous semidirect product(C43⋊C3)⋊(C4×C11⋊C5)
unambiguous semidirect productDic43⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×(C43⋊C3)⋊C4)⋊C5
unambiguous semidirect product(C11⋊C5×Dic43)⋊C3

Splittings

derived, HallC11×C43 ⋊ C3×C4×C5
HallC11⋊C5×Dic43 ⋊ C3
HallC11⋊C5×C43⋊C3 ⋊ C4
HallC11×(C43⋊C3)⋊C4 ⋊ C5
HallC43×C11⋊C5 ⋊ C3×C4
HallC11×Dic43 ⋊ C3×C5
HallC11×C43⋊C3 ⋊ C4×C5
HallDic43 ⋊ C3×C11⋊C5
HallC43⋊C3 ⋊ C4×C11⋊C5
SylowC43 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C5×(C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D43⋊C3
commutator, hypocenterC11×C43C3×C4×C5
Fitting, socle, cosocleC2×C11×C43C2×C3×C5
prime radicalC2×C11⋊C5×C43⋊C3C2
LCSG ▷ C11×C43
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1892

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 34);