Finite Group Databasebeta

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C7×D2325 #45654387

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

Aliases

direct productC7×D2325
unambiguous semidirect productC3⋊(C7×D775)
unambiguous semidirect productC25⋊(C7×D93)
unambiguous semidirect productC31⋊(C7×D75)

Splittings

Fitting, HallC3×C7×C25×C31 ⋊ C2
derived, HallC3×C25×C31 ⋊ C2×C7
HallC7×C25×C31 ⋊ D3
HallC25×C31 ⋊ D3×C7
HallC3×C7×C31 ⋊ D25
HallC3×C7×C25 ⋊ D31
HallC7×C31 ⋊ D75
HallC7×C25 ⋊ D93
HallC3×C31 ⋊ C7×D25
HallC3×C25 ⋊ C7×D31
SylowC31 ⋊ C7×D75
SylowC25 ⋊ C7×D93
HallC3×C7 ⋊ D775
SylowC3 ⋊ C7×D775

Subgroups

subgroupG/H
center, hypercenterC7D2325
commutator, cosocle, hypocenterC3×C25×C31C2×C7
FrattiniC5C7×D465
FittingC3×C7×C25×C31C2
socleC3×C5×C7×C31D5
LCSG ▷ C3×C25×C31
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16275

Conjugacy classes & character table

8148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 23);