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C43×C3⋊#63121 #46776565

order33540
automorphism?
homologyAbelianization (H1) = C4×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×C3⋊#63121
unambiguous semidirect productC3⋊(C43×#63121)

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C43
HallC5×C13×C43 ⋊ Dic3
HallC3×C13×C43 ⋊ AGL(1,𝔽5)
HallC3×C5×C43 ⋊ #261
HallC13×C43 ⋊ ΓL(1,𝔽16)
HallC5×C43 ⋊ C3⋊#261
HallC3×C43 ⋊ #63121
HallC5×C13 ⋊ Dic3×C43
HallC3×C13 ⋊ AGL(1,𝔽5)×C43
HallC3×C5 ⋊ C43×#261
SylowC13 ⋊ C43×ΓL(1,𝔽16)
SylowC5 ⋊ C43×C3⋊#261
SylowC3 ⋊ C43×#63121

Subgroups

subgroupG/H
center, hypercenterC43C3⋊#63121
commutator, hypocenterC3×C5×C13C4×C43
FrattiniC1G
Fitting, socleC3×C5×C13×C43C4
prime radicalC3×C43×D65C2
cosocleC3×D65C2×C43
LCSG ▷ C3×C5×C13
UCSC1 ◁ C43

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

2322 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 185);