Finite Group Databasebeta

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C41×#1043⋊C9 #49146800

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

Aliases

direct productC41×#1043⋊C9
unambiguous semidirect product#1043⋊(C9×C41)
unambiguous semidirect product(C41×#1043)⋊C9

Splittings

derived, SylowC52 ⋊ C4×C9×C41
HallC41×C52⋊C9 ⋊ C4
HallC41×#1043 ⋊ C9
HallC52×C41 ⋊ C4×C9
HallC52⋊C9 ⋊ C4×C41
Hall#1043 ⋊ C9×C41

Subgroups

subgroupG/H
center, hypercenterC3×C41#1043⋊C3
commutator, hypocenterC52C4×C9×C41
FrattiniC3C41×#1043⋊C3
Fitting, socleC3×C52×C41C3×C4
prime radicalC3×C41×C5⋊D5C2×C3
cosocleC3×C5⋊D5C2×C3×C41
LCSG ▷ C52
UCSC1 ◁ C3×C41

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1845

Conjugacy classes & character table

1722 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 201);