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D3×(C31⋊C3)⋊C25 #28358379

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

Aliases

direct productD3×(C31⋊C3)⋊C25
unambiguous semidirect productC3⋊(C2×(C31⋊C3)⋊C25)
unambiguous semidirect product(D3×C31⋊C3)⋊C25
unambiguous semidirect product(D3×C31⋊C25)⋊C3

Splittings

derivedC3×C31 ⋊ C2×C3×C25
HallC3×(C31⋊C3)⋊C25 ⋊ C2
HallC31⋊C25 ⋊ C3×D3
HallD3×C31⋊C3 ⋊ C25
HallC3×C31⋊C3 ⋊ C2×C25
SylowC31 ⋊ C3×D3×C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC5D3×(C31⋊C3)⋊C5
commutator, hypocenterC3×C31C2×C3×C25
Fitting, socle, cosocleC3×C5×C31C2×C3×C5
prime radicalC5×D3×C31⋊C3C5
LCSG ▷ C3×C31
UCSC1 ◁ C5

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×(D31⋊C3)⋊C25, C2×D3×(C31⋊C3)⋊C25
maximal normal subgroup ofD3×(D31⋊C3)⋊C25, C2×D3×(C31⋊C3)⋊C25
maximal quotient ofDic3×(C31⋊C3)⋊C25, C2×D3×(C31⋊C3)⋊C25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 22);