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C23×C3⋊(C11⋊AGL(1,𝔽5)) #29503303

order15180
automorphism?
homologyAbelianization (H1) = C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C23×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C23×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C11×C23 ⋊ C4
derived, HallC3×C5×C11 ⋊ C4×C23
HallC5×C11×C23 ⋊ Dic3
HallC3×C11×C23 ⋊ AGL(1,𝔽5)
HallC3×C5×C23 ⋊ Dic11
HallC11×C23 ⋊ ΓL(1,𝔽16)
HallC5×C23 ⋊ Dic33
HallC3×C23 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C23
HallC3×C11 ⋊ AGL(1,𝔽5)×C23
HallC3×C5 ⋊ C23×Dic11
SylowC11 ⋊ C23×ΓL(1,𝔽16)
SylowC5 ⋊ C23×Dic33
SylowC3 ⋊ C23×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC23C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C23
FrattiniC1G
Fitting, socleC3×C5×C11×C23C4
prime radicalC3×D5×C11×C23C2
cosocleC3×D5×C11C2×C23
LCSG ▷ C3×C5×C11
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1587 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 89);