Finite Group Databasebeta

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C3×C7⋊#10596817 #27131766

order12180
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊#10596817

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C4
derived, HallC5×C7×C29 ⋊ C3×C4
HallC3×C7×C29 ⋊ Dic5
HallC3×C5×C29 ⋊ Dic7
HallC7×C29 ⋊ C3×Dic5
HallC5×C29 ⋊ C3×Dic7
HallC3×C5×C7 ⋊ #1181
HallC3×C29 ⋊ Dic35
HallC5×C7 ⋊ C3×#1181
SylowC29 ⋊ C3×Dic35
HallC3×C7 ⋊ #10596817
HallC3×C5 ⋊ C7⋊#1181
SylowC7 ⋊ C3×#10596817
SylowC5 ⋊ C3×C7⋊#1181

Subgroups

subgroupG/H
center, hypercenterC3C7⋊#10596817
commutator, hypocenterC5×C7×C29C3×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C29C4
LCSG ▷ C5×C7×C29
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

849 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C7⋊C9)⋊#10596817, C9×C7⋊#10596817, C3×ΓL(1,𝔽8)⋊#10596817, …
maximal normal subgroup of(C7⋊C9)⋊#10596817, C9×C7⋊#10596817, C3×ΓL(1,𝔽8)⋊#10596817, …
maximal quotient ofC9×C7⋊#10596817, C32×C7⋊#10596817, C3×C3⋊(C7⋊#10596817)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 101);