Finite Group Databasebeta

← Prev (#27131773) Next (#27131775) →

C5×C3⋊(C7⋊#1181) #27131774

order12180
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C7⋊#1181)
unambiguous semidirect productC3⋊(C5×C7⋊#1181)
unambiguous semidirect productC7⋊(C5×C3⋊#1181)

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C4
derived, HallC3×C7×C29 ⋊ C4×C5
HallC5×C7×C29 ⋊ Dic3
HallC3×C5×C29 ⋊ Dic7
HallC7×C29 ⋊ C5×Dic3
HallC5×C29 ⋊ Dic21
HallC3×C5×C7 ⋊ #1181
HallC3×C29 ⋊ C5×Dic7
HallC5×C7 ⋊ C3⋊#1181
SylowC29 ⋊ C5×Dic21
HallC3×C7 ⋊ C5×#1181
HallC3×C5 ⋊ C7⋊#1181
SylowC7 ⋊ C5×C3⋊#1181
SylowC3 ⋊ C5×C7⋊#1181

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C7⋊#1181)
commutator, hypocenterC3×C7×C29C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C29C4
LCSG ▷ C3×C7×C29
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7⋊(C9⋊#1181), C5×C3⋊(ΓL(1,𝔽8)⋊#1181), C3×C5×C3⋊(C7⋊#1181), …
maximal normal subgroup ofC5×C3⋊(ΓL(1,𝔽8)⋊#1181), C3×C5×C3⋊(C7⋊#1181)
maximal quotient ofC5×C7⋊(C9⋊#1181), C3×C5×C3⋊(C7⋊#1181), C5×C3⋊(C3⋊(C7⋊#1181))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 109);