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C3×C3⋊(D31⋊C25) #28358382

order13950
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(D31⋊C25)
unambiguous semidirect productC3⋊(C3×D31⋊C25)
unambiguous semidirect product(C3×D93)⋊C25

Splittings

derivedC3×C31 ⋊ C2×C3×C25
HallC32×C31⋊C25 ⋊ C2
HallC31⋊C25 ⋊ C3×D3
HallC3×D93 ⋊ C25
HallC32×C31 ⋊ C2×C25
SylowC31 ⋊ C3×D3×C25
SylowC32 ⋊ D31⋊C25

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊(D31⋊C5)
commutator, hypocenterC3×C31C2×C3×C25
FrattiniC5C3×C3⋊(D31⋊C5)
Fitting, socleC32×C5×C31C2×C5
prime radicalC3×C5×D93C5
cosocleC3×C5×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C3×C5

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D31⋊C25, D3×C3⋊(D31⋊C25), (C3⋊D3)⋊(D31⋊C25), …
maximal normal subgroup ofC3×D3×D31⋊C25, D3×C3⋊(D31⋊C25), (C3⋊D3)⋊(D31⋊C25), …
maximal quotient ofC3×C3⋊(Dic31⋊C25), C2×C3×C3⋊(D31⋊C25)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 25);