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C52×D3×C31⋊C3 #28358486

order13950
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×D3×C31⋊C3
unambiguous semidirect productC3⋊(C2×C52×C31⋊C3)

Splittings

Fitting, socleC3×C52×C31 ⋊ C2×C3
derivedC3×C31 ⋊ C2×C3×C52
HallC3×C52×C31⋊C3 ⋊ C2
HallC52×C31 ⋊ C3×D3
HallC3×C31⋊C3 ⋊ C2×C52
SylowC31 ⋊ C3×C52×D3

Subgroups

subgroupG/H
center, hypercenterC52D3×C31⋊C3
commutator, cosocle, hypocenterC3×C31C2×C3×C52
FrattiniC1G
Fitting, socleC3×C52×C31C2×C3
LCSG ▷ C3×C31
UCSC1 ◁ C52

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC52×D3×D31⋊C3, C5×D3×C5⋊(D31⋊C3), C5×D3×D5×C31⋊C3, …
maximal normal subgroup ofC52×D3×D31⋊C3, C5×D3×C5⋊(D31⋊C3), C5×D3×D5×C31⋊C3, …
maximal quotient ofC52×Dic3×C31⋊C3, C2×C52×D3×C31⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 129);