Finite Group Databasebeta

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C9×C37×#1035 #45685752

order33300
automorphism?
homologyAbelianization (H1) = C4×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC9×C37×#1035

Splittings

Fitting, HallC9×C25×C37 ⋊ C4
derived, SylowC25 ⋊ C4×C9×C37
HallC25×C37 ⋊ C4×C9
HallC9×C25 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC9×C37#1035
commutator, hypocenterC25C4×C9×C37
FrattiniC3×C5C3×AGL(1,𝔽5)×C37
FittingC9×C25×C37C4
socleC3×C5×C37C3×AGL(1,𝔽5)
prime radicalC3×C37×D25C2×C3
cosocleC3×D25C2×C3×C37
LCSG ▷ C25
UCSC1 ◁ C9×C37

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8325

Conjugacy classes & character table

3330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 25);