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C5×C7×C3⋊#1181 #27131772

order12180
isoclinismisoclinic class of C3⋊#1181
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊#1181
commutator, hypocenterC3×C29C4×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C29C4
LCSG ▷ C3×C29
UCSC1 ◁ C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

945 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 107);