Finite Group Databasebeta

← Prev (#46776408) Next (#46776410) →

C5×(C43⋊C3)⋊Dic13 #46776409

order33540
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C43⋊C3)⋊Dic13
unambiguous semidirect product(C43⋊C3)⋊(C5×Dic13)

Splittings

derived, HallC13×C43 ⋊ C3×C4×C5
HallC5×Dic559 ⋊ C3
HallC5×C13×C43⋊C3 ⋊ C4
HallC5×C13×C43 ⋊ C3×C4
HallDic559 ⋊ C3×C5
HallC13×C43⋊C3 ⋊ C4×C5
HallC5×C43⋊C3 ⋊ Dic13
HallC5×C43 ⋊ C3×Dic13
HallC43⋊C3 ⋊ C5×Dic13
HallC5×C13 ⋊ (C43⋊C3)⋊C4
SylowC43 ⋊ C3×C5×Dic13
SylowC13 ⋊ C5×(C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5(C43⋊C3)⋊D13
commutator, hypocenterC13×C43C3×C4×C5
FrattiniC2C5×(C43⋊C3)⋊D13
Fitting, socleC2×C5×C13×C43C2×C3
prime radicalC2×C5×C13×C43⋊C3C2
cosocleC2×C13×C43C2×C3×C5
LCSG ▷ C13×C43
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11180

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 29);