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C3×C5×C5⋊(D31⋊C3) #28358473

order13950
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C5⋊(D31⋊C3)
unambiguous semidirect productC5⋊(C3×C5×D31⋊C3)
unambiguous semidirect product(C5×D155)⋊C32
unambiguous semidirect product(C3×C5×D155)⋊C3

Splittings

Fitting, socleC3×C52×C31 ⋊ C2×C3
derivedC5×C31 ⋊ C2×C32×C5
HallC3×C52×C31⋊C3 ⋊ C2
HallC5×D155 ⋊ C32
HallC52×C31 ⋊ C2×C32
HallC3×C31⋊C3 ⋊ C5×D5
SylowC31 ⋊ C32×C5×D5
SylowC52 ⋊ C3×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5C5⋊(D31⋊C3)
commutator, cosocle, hypocenterC5×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C52×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

555 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D5×D31⋊C3, C3×D5×C5⋊(D31⋊C3), C3×(C5⋊(D31⋊C3))⋊D5, …
maximal normal subgroup ofC3×C5×D5×D31⋊C3, C3×D5×C5⋊(D31⋊C3), C3×(C5⋊(D31⋊C3))⋊D5, …
maximal quotient ofC3×C5×(C31⋊C3)⋊Dic5, C2×C3×C5×C5⋊(D31⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 116);