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C3×C11×C23⋊AGL(1,𝔽5) #29503286

order15180
isoclinismisoclinic class of C23⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C23⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C11×C23 ⋊ C4
derived, HallC5×C23 ⋊ C3×C4×C11
HallC5×C11×C23 ⋊ C3×C4
HallC3×C11×C23 ⋊ AGL(1,𝔽5)
HallC3×C5×C23 ⋊ C4×C11
HallC11×C23 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C11 ⋊ Dic23
HallC3×C23 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C3×Dic23
SylowC23 ⋊ C3×C11×AGL(1,𝔽5)
HallC3×C5 ⋊ C11×Dic23
SylowC5 ⋊ C3×C11×Dic23

Subgroups

subgroupG/H
center, hypercenterC3×C11C23⋊AGL(1,𝔽5)
commutator, hypocenterC5×C23C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C23C4
prime radicalC3×D5×C11×C23C2
cosocleD5×C23C2×C3×C11
LCSG ▷ C5×C23
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 72);