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C31⋊C3×C3⋊(C5⋊D5) #28358490

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

Aliases

direct productC31⋊C3×C3⋊(C5⋊D5)
unambiguous semidirect productC3⋊(C5⋊D5×C31⋊C3)
unambiguous semidirect productC5⋊(D15×C31⋊C3)

Splittings

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

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C31C2×C3
LCSG ▷ C3×C52×C31
UCSC1

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

507 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C5⋊(D31⋊C3))⋊D15, D5×D15×C31⋊C3, C3⋊(C5⋊D5)×D31⋊C3, …
maximal normal subgroup of(C5⋊(D31⋊C3))⋊D15, D5×D15×C31⋊C3, C3⋊(C5⋊D5)×D31⋊C3, …
maximal quotient ofC31⋊C3×C3⋊#1039, C2×C31⋊C3×C3⋊(C5⋊D5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 133);