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C11×C3⋊(C23⋊AGL(1,𝔽5)) #29503302

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

Aliases

direct productC11×C3⋊(C23⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C11×C23⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C11×C23 ⋊ C4
derived, HallC3×C5×C23 ⋊ C4×C11
HallC5×C11×C23 ⋊ Dic3
HallC3×C11×C23 ⋊ AGL(1,𝔽5)
HallC11×C23 ⋊ ΓL(1,𝔽16)
HallC3×C5×C11 ⋊ Dic23
HallC5×C23 ⋊ C11×Dic3
HallC3×C23 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ Dic69
HallC3×C11 ⋊ C23⋊AGL(1,𝔽5)
SylowC23 ⋊ C11×ΓL(1,𝔽16)
HallC3×C5 ⋊ C11×Dic23
SylowC5 ⋊ C11×Dic69
SylowC3 ⋊ C11×C23⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C23⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C23C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C23C4
prime radicalC3×D5×C11×C23C2
cosocleC3×D5×C23C2×C11
LCSG ▷ C3×C5×C23
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1551 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 88);