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C3×C11⋊(C23⋊AGL(1,𝔽5)) #29503288

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

Aliases

direct productC3×C11⋊(C23⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C3×C23⋊AGL(1,𝔽5))
unambiguous semidirect productC23⋊(C3×C11⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C11×C23 ⋊ C4
derived, HallC5×C11×C23 ⋊ C3×C4
HallC3×C11×C23 ⋊ AGL(1,𝔽5)
HallC3×C5×C23 ⋊ Dic11
HallC11×C23 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C11 ⋊ Dic23
HallC5×C23 ⋊ C3×Dic11
HallC3×C23 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ C3×Dic23
HallC3×C11 ⋊ C23⋊AGL(1,𝔽5)
SylowC23 ⋊ C3×C11⋊AGL(1,𝔽5)
HallC3×C5 ⋊ Dic253
SylowC11 ⋊ C3×C23⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×Dic253

Subgroups

subgroupG/H
center, hypercenterC3C11⋊(C23⋊AGL(1,𝔽5))
commutator, hypocenterC5×C11×C23C3×C4
FrattiniC1G
Fitting, socleC3×C5×C11×C23C4
prime radicalC3×D5×C11×C23C2
cosocleD5×C11×C23C2×C3
LCSG ▷ C5×C11×C23
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1527 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 74);