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C5×C3⋊(C5⋊(D31⋊C3)) #28358487

order13950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C5⋊(D31⋊C3))
unambiguous semidirect productC3⋊(C5×C5⋊(D31⋊C3))
unambiguous semidirect productC5⋊(C5×C3⋊(D31⋊C3))
unambiguous semidirect product(C5×D465)⋊C3

Splittings

Fitting, socleC3×C52×C31 ⋊ C2×C3
derivedC3×C5×C31 ⋊ C2×C3×C5
HallC3×C52×C31⋊C3 ⋊ C2
HallC52×C31 ⋊ C3×D3
HallC3×C31⋊C3 ⋊ C5×D5
SylowC31 ⋊ C3×C5×D15
SylowC52 ⋊ C3⋊(D31⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C5⋊(D31⋊C3))
commutator, cosocle, hypocenterC3×C5×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C31C2×C3
LCSG ▷ C3×C5×C31
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

510 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D15×D31⋊C3, C5×D5×C3⋊(D31⋊C3), C5×D3×C5⋊(D31⋊C3), …
maximal normal subgroup ofC5×D15×D31⋊C3, C5×D5×C3⋊(D31⋊C3), C5×D3×C5⋊(D31⋊C3), …
maximal quotient ofC5×C3⋊((C31⋊C3)⋊Dic5), C2×C5×C3⋊(C5⋊(D31⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 130);