Finite Group Databasebeta

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C2×C3×C25×C31⋊C3 #28358394

order13950
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C25 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C25×C31⋊C3
unambiguous semidirect product(C2×C25×C31)⋊C32
unambiguous semidirect product(C2×C3×C25×C31)⋊C3

Splittings

FittingC2×C3×C25×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C32×C25
HallC2×C25×C31 ⋊ C32
HallC25×C31 ⋊ C2×C32
HallC2×C31 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25C31⋊C3
commutator, hypocenterC31C2×C32×C25
FrattiniC5C2×C3×C5×C31⋊C3
FittingC2×C3×C25×C31C3
socleC2×C3×C5×C31C3×C5
prime radicalC2×C3×C5×C31⋊C3C5
cosocleC5×C31C2×C32×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C25×(C31⋊C3)⋊C4, C3×(C31⋊C3)⋊Dic25, C3×C31⋊C3×Dic25, …
maximal normal subgroup ofC3×C25×(C31⋊C3)⋊C4, C3×(C31⋊C3)⋊Dic25, C3×C31⋊C3×Dic25, …
maximal quotient ofC3×C4×C25×C31⋊C3, C22×C3×C25×C31⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 37);