Finite Group Databasebeta

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C9×C37×#1044 #45686007

order33300
automorphism?
homologyAbelianization (H1) = C4×C9×C37 · Schur multiplier (H2) = C5

Aliases

direct productC9×C37×#1044

Splittings

Fitting, HallC52×C9×C37 ⋊ C4
derived, SylowC52 ⋊ C4×C9×C37
HallC52×C37 ⋊ C4×C9
HallC52×C9 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC9×C37#1044
commutator, hypocenterC52C4×C9×C37
FrattiniC3C3×C37×#1044
FittingC52×C9×C37C4
socleC3×C52×C37C3×C4
prime radicalC3×C37×C5⋊D5C2×C3
cosocleC3×C5⋊D5C2×C3×C37
LCSG ▷ C52
UCSC1 ◁ C9×C37

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3330

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, 280);