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C3×C3⋊(C7⋊#1181) #20300647

order7308
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC32×C7×C29 ⋊ C4
derivedC3×C7×C29 ⋊ C3×C4
HallC32×C29 ⋊ Dic7
HallC7×C29 ⋊ C3×Dic3
HallC32×C7 ⋊ #1181
SylowC29 ⋊ C3×Dic21
SylowC32 ⋊ C7⋊#1181
SylowC7 ⋊ C3×C3⋊#1181

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C7⋊#1181)
commutator, hypocenterC3×C7×C29C3×C4
FrattiniC1G
Fitting, socleC32×C7×C29C4
LCSG ▷ C3×C7×C29
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C3⋊(C7⋊#1181), C3×C3⋊(C7⋊#10596814), C3×C3⋊(C7⋊#10596815), …
maximal normal subgroup ofC3×C5×C3⋊(C7⋊#1181)
maximal quotient ofC3×C5×C3⋊(C7⋊#1181), C3×C3⋊(C7⋊#10596814), C3×C3⋊(C7⋊#10596815), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 122);