Finite Group Databasebeta

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C7×D25×C31⋊C3 #45654409

order32550
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D25×C31⋊C3
unambiguous semidirect productC25⋊(C2×C7×C31⋊C3)
unambiguous semidirect product(C31×D25)⋊(C3×C7)

Splittings

Fitting, HallC7×C25×C31 ⋊ C2×C3
derived, HallC25×C31 ⋊ C2×C3×C7
HallC7×C25×C31⋊C3 ⋊ C2
HallC7×C31×D25 ⋊ C3
HallC25×C31⋊C3 ⋊ C2×C7
HallC31×D25 ⋊ C3×C7
HallC7×C31 ⋊ C3×D25
HallC7×C25 ⋊ C2×C31⋊C3
SylowC31 ⋊ C3×C7×D25
SylowC25 ⋊ C2×C7×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D25×C31⋊C3
commutator, cosocle, hypocenterC25×C31C2×C3×C7
FrattiniC5C7×D5×C31⋊C3
FittingC7×C25×C31C2×C3
socleC5×C7×C31C3×D5
LCSG ▷ C25×C31
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5425

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 45);