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C5×C3⋊(Dic23⋊C11) #29503237

order15180
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(Dic23⋊C11)
unambiguous semidirect productC3⋊(C5×Dic23⋊C11)
unambiguous semidirect product(C23⋊C11)⋊(C5×Dic3)
unambiguous semidirect productDic69⋊(C5×C11)
unambiguous semidirect product(C5×Dic69)⋊C11

Splittings

derived, HallC3×C23 ⋊ C4×C5×C11
HallC3×C5×C23⋊C11 ⋊ C4
HallC5×Dic69 ⋊ C11
HallC5×C23⋊C11 ⋊ Dic3
HallC3×C23⋊C11 ⋊ C4×C5
HallC3×C5×C23 ⋊ C4×C11
HallDic69 ⋊ C5×C11
HallC23⋊C11 ⋊ C5×Dic3
HallC5×C23 ⋊ C11×Dic3
SylowC23 ⋊ C5×C11×Dic3
HallC3×C5 ⋊ Dic23⋊C11
SylowC3 ⋊ C5×Dic23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊AGL(1,𝔽23)
commutator, hypocenterC3×C23C4×C5×C11
FrattiniC2C5×C3⋊AGL(1,𝔽23)
Fitting, socleC2×C3×C5×C23C2×C11
prime radicalC2×C3×C5×C23⋊C11C2
cosocleC2×C3×C23C2×C5×C11
LCSG ▷ C3×C23
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1380

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 23);