Finite Group Databasebeta

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C3×C43⋊#63120 #46776544

order33540
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C43⋊#63120

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C4
derived, HallC5×C13×C43 ⋊ C3×C4
HallC3×C13×C43 ⋊ AGL(1,𝔽5)
HallC3×C5×C43 ⋊ Dic13
HallC13×C43 ⋊ C3×AGL(1,𝔽5)
HallC5×C43 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ Dic43
HallC3×C43 ⋊ #63120
HallC5×C13 ⋊ C3×Dic43
SylowC43 ⋊ C3×#63120
HallC3×C13 ⋊ C43⋊AGL(1,𝔽5)
HallC3×C5 ⋊ Dic559
SylowC13 ⋊ C3×C43⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×Dic559

Subgroups

subgroupG/H
center, hypercenterC3C43⋊#63120
commutator, hypocenterC5×C13×C43C3×C4
FrattiniC1G
Fitting, socleC3×C5×C13×C43C4
prime radicalC3×D5×C13×C43C2
cosocleD5×C13×C43C2×C3
LCSG ▷ C5×C13×C43
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

3363 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 164);