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C23×C3⋊(Dic11⋊C5) #29503245

order15180
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊(Dic11⋊C5)
unambiguous semidirect productC3⋊(C23×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(Dic3×C23)
unambiguous semidirect productDic33⋊(C5×C23)
unambiguous semidirect product(C23×Dic33)⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C5×C23
HallC3×C23×C11⋊C5 ⋊ C4
HallC23×Dic33 ⋊ C5
HallC23×C11⋊C5 ⋊ Dic3
HallC3×C11×C23 ⋊ C4×C5
HallC11×C23 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ C4×C23
HallDic33 ⋊ C5×C23
HallC3×C23 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic3×C23
SylowC11 ⋊ C5×Dic3×C23
SylowC3 ⋊ C23×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C5×C23
FrattiniC2C23×C3⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C23C2×C5
prime radicalC2×C3×C23×C11⋊C5C2
cosocleC2×C3×C11C2×C5×C23
LCSG ▷ C3×C11
UCSC1 ◁ C2×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 31);