Finite Group Databasebeta

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C9×C37×D25 #30659205

order16650
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC9×C37×D25
unambiguous semidirect productC25⋊(C2×C9×C37)

Splittings

Fitting, HallC9×C25×C37 ⋊ C2
derived, SylowC25 ⋊ C2×C9×C37
HallC25×C37 ⋊ C2×C9
HallC9×C25 ⋊ C2×C37

Subgroups

subgroupG/H
center, hypercenterC9×C37D25
commutator, hypocenterC25C2×C9×C37
FrattiniC3×C5C3×D5×C37
FittingC9×C25×C37C2
socleC3×C5×C37C3×D5
prime radicalC3×C37×D25C3
cosocleC3×C25C2×C3×C37
LCSG ▷ C25
UCSC1 ◁ C9×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8325

Conjugacy classes & character table

4662 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C37×#1035, C9×#16814856, C9×D25×D37, …
maximal normal subgroup ofC9×C37×#1035, C9×#16814856, C9×D25×D37, …
maximal quotient ofC9×C37×Dic25, C2×C9×C37×D25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 7);