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C25×#13093366 #49150205

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×#13093366

Splittings

Fitting, HallC13×C19×C25 ⋊ C2×C3
derived, HallC13×C19 ⋊ C2×C3×C25
HallC25×#10625202 ⋊ C2
HallC25×D247 ⋊ C3
Hall#10625202 ⋊ C2×C25
HallD247 ⋊ C3×C25
HallC19×C25 ⋊ D13⋊C3
HallC13×C25 ⋊ D19⋊C3
SylowC19 ⋊ C25×D13⋊C3
SylowC13 ⋊ C25×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC25#13093366
commutator, hypocenterC13×C19C2×C3×C25
FrattiniC5C5×#13093366
FittingC13×C19×C25C2×C3
socle, cosocleC5×C13×C19C2×C3×C5
prime radicalC5×#13093366C5
LCSG ▷ C13×C19
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

1175 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 31);