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C3×C23⋊(Dic11⋊C5) #29503242

order15180
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23⋊(Dic11⋊C5)
unambiguous semidirect productC23⋊(C3×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic23)
unambiguous semidirect productDic253⋊(C3×C5)
unambiguous semidirect product(C3×Dic253)⋊C5

Splittings

derived, HallC11×C23 ⋊ C3×C4×C5
HallC3×C23×C11⋊C5 ⋊ C4
HallC3×Dic253 ⋊ C5
HallC23×C11⋊C5 ⋊ C3×C4
HallDic253 ⋊ C3×C5
HallC3×C11×C23 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ Dic23
HallC3×C23 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×Dic23
HallC3×C11 ⋊ C5×Dic23
SylowC23 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C3×C5×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3C23⋊AGL(1,𝔽11)
commutator, hypocenterC11×C23C3×C4×C5
FrattiniC2C3×C23⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C23C2×C5
prime radicalC2×C3×C23×C11⋊C5C2
cosocleC2×C11×C23C2×C3×C5
LCSG ▷ C11×C23
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 28);