Finite Group Databasebeta

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C25×C31×D21 #45654384

order32550
automorphism?
homologyAbelianization (H1) = C2×C25×C31 · Schur multiplier (H2) = C1

Aliases

direct productC25×C31×D21
unambiguous semidirect productC3⋊(D7×C25×C31)
unambiguous semidirect productC7⋊(D3×C25×C31)

Splittings

Fitting, HallC3×C7×C25×C31 ⋊ C2
derived, HallC3×C7 ⋊ C2×C25×C31
HallC7×C25×C31 ⋊ D3
HallC3×C25×C31 ⋊ D7
HallC3×C7×C31 ⋊ C2×C25
HallC3×C7×C25 ⋊ C2×C31
HallC7×C31 ⋊ D3×C25
HallC7×C25 ⋊ D3×C31
HallC3×C31 ⋊ D7×C25
HallC3×C25 ⋊ D7×C31
SylowC7 ⋊ D3×C25×C31
SylowC3 ⋊ D7×C25×C31

Subgroups

subgroupG/H
center, hypercenterC25×C31D21
commutator, hypocenterC3×C7C2×C25×C31
FrattiniC5C5×C31×D21
FittingC3×C7×C25×C31C2
socleC3×C5×C7×C31C2×C5
prime radicalC5×C31×D21C5
cosocleC3×C5×C7C2×C5×C31
LCSG ▷ C3×C7
UCSC1 ◁ C25×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16275

Conjugacy classes & character table

9300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 20);