Finite Group Databasebeta

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C9×C41×#1043 #49146830

order36900
automorphism?
homologyAbelianization (H1) = C4×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productC9×C41×#1043

Splittings

Fitting, HallC52×C9×C41 ⋊ C4
derived, SylowC52 ⋊ C4×C9×C41
HallC52×C41 ⋊ C4×C9
HallC52×C9 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC9×C41#1043
commutator, hypocenterC52C4×C9×C41
FrattiniC3C3×C41×#1043
FittingC52×C9×C41C4
socleC3×C52×C41C3×C4
prime radicalC3×C41×C5⋊D5C2×C3
cosocleC3×C5⋊D5C2×C3×C41
LCSG ▷ C52
UCSC1 ◁ C9×C41

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9225

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 231);