Finite Group Databasebeta

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C7×C25×D31⋊C3 #45654397

order32550
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×D31⋊C3
unambiguous semidirect product(C25×D31)⋊(C3×C7)

Splittings

Fitting, HallC7×C25×C31 ⋊ C2×C3
derived, SylowC31 ⋊ C2×C3×C7×C25
HallC7×C25×C31⋊C3 ⋊ C2
HallC7×C25×D31 ⋊ C3
HallC25×C31⋊C3 ⋊ C2×C7
HallC25×D31 ⋊ C3×C7
HallC25×C31 ⋊ C2×C3×C7
HallC7×C31⋊C3 ⋊ C2×C25
HallC7×D31 ⋊ C3×C25
HallC7×C31 ⋊ C2×C3×C25
HallC31⋊C3 ⋊ C2×C7×C25
HallD31 ⋊ C3×C7×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25D31⋊C3
commutator, hypocenterC31C2×C3×C7×C25
FrattiniC5C5×C7×D31⋊C3
FittingC7×C25×C31C2×C3
socleC5×C7×C31C2×C3×C5
prime radicalC5×C7×D31⋊C3C5
cosocleC5×C31C2×C3×C5×C7
LCSG ▷ C31
UCSC1 ◁ C7×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5425

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 33);