Finite Group Databasebeta

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C7×C3⋊#10596817 #27131788

order12180
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊#10596817
unambiguous semidirect productC3⋊(C7×#10596817)

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C4
derived, HallC3×C5×C29 ⋊ C4×C7
HallC5×C7×C29 ⋊ Dic3
HallC3×C7×C29 ⋊ Dic5
HallC7×C29 ⋊ Dic15
HallC5×C29 ⋊ C7×Dic3
HallC3×C5×C7 ⋊ #1181
HallC3×C29 ⋊ C7×Dic5
HallC5×C7 ⋊ C3⋊#1181
SylowC29 ⋊ C7×Dic15
HallC3×C7 ⋊ #10596817
HallC3×C5 ⋊ C7×#1181
SylowC5 ⋊ C7×C3⋊#1181
SylowC3 ⋊ C7×#10596817

Subgroups

subgroupG/H
center, hypercenterC7C3⋊#10596817
commutator, hypocenterC3×C5×C29C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C29C4
LCSG ▷ C3×C5×C29
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

861 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C9⋊#10596817, ΓL(1,𝔽8)×C3⋊#10596817, C3×C7×C3⋊#10596817, …
maximal normal subgroup ofΓL(1,𝔽8)×C3⋊#10596817, C3×C7×C3⋊#10596817
maximal quotient ofC7×C9⋊#10596817, C3×C7×C3⋊#10596817, C7×C3⋊(C3⋊#10596817)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 123);