Finite Group Databasebeta

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C3×C5×Dic23⋊C11 #29503233

order15180
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic23⋊C11
unambiguous semidirect productDic23⋊(C3×C5×C11)
unambiguous semidirect product(C23⋊C11)⋊(C3×C4×C5)
unambiguous semidirect product(C3×Dic23)⋊(C5×C11)
unambiguous semidirect product(C5×Dic23)⋊(C3×C11)
unambiguous semidirect product(C3×C5×Dic23)⋊C11

Splittings

derived, SylowC23 ⋊ C3×C4×C5×C11
HallC3×C5×C23⋊C11 ⋊ C4
HallC3×C5×Dic23 ⋊ C11
HallC5×C23⋊C11 ⋊ C3×C4
HallC3×C23⋊C11 ⋊ C4×C5
HallC5×Dic23 ⋊ C3×C11
HallC3×C5×C23 ⋊ C4×C11
HallC3×Dic23 ⋊ C5×C11
HallC23⋊C11 ⋊ C3×C4×C5
HallC5×C23 ⋊ C3×C4×C11
HallDic23 ⋊ C3×C5×C11
HallC3×C23 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5AGL(1,𝔽23)
commutator, hypocenterC23C3×C4×C5×C11
FrattiniC2C3×C5×AGL(1,𝔽23)
Fitting, socleC2×C3×C5×C23C2×C11
prime radicalC2×C3×C5×C23⋊C11C2
cosocleC2×C23C2×C3×C5×C11
LCSG ▷ C23
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1380

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 19);