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C3×C25×D217 #45654377

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

Aliases

direct productC3×C25×D217

Splittings

Fitting, HallC3×C7×C25×C31 ⋊ C2
derived, HallC7×C31 ⋊ C2×C3×C25
HallC7×C25×C31 ⋊ C2×C3
HallC3×C25×C31 ⋊ D7
HallC25×C31 ⋊ C3×D7
HallC3×C7×C31 ⋊ C2×C25
HallC3×C7×C25 ⋊ D31
HallC7×C25 ⋊ C3×D31
HallC3×C31 ⋊ D7×C25
SylowC31 ⋊ C3×D7×C25
HallC3×C7 ⋊ C25×D31
SylowC7 ⋊ C3×C25×D31

Subgroups

subgroupG/H
center, hypercenterC3×C25D217
commutator, hypocenterC7×C31C2×C3×C25
FrattiniC5C3×C5×D217
FittingC3×C7×C25×C31C2
socleC3×C5×C7×C31C2×C5
prime radicalC3×C5×D217C5
cosocleC5×C7×C31C2×C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C3×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16275

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 13);