Finite Group Databasebeta

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C2×C41×C49⋊C9 #49116263

order36162
automorphism?
homologyAbelianization (H1) = C2×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productC2×C41×C49⋊C9
unambiguous semidirect product(C2×C49)⋊(C9×C41)
unambiguous semidirect product(C2×C41×C49)⋊C9

Splittings

derived, SylowC49 ⋊ C2×C9×C41
HallC2×C41×C49 ⋊ C9
HallC41×C49 ⋊ C2×C9
HallC2×C49 ⋊ C9×C41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C41C49⋊C3
commutator, hypocenterC49C2×C9×C41
FrattiniC3×C7C2×ΓL(1,𝔽8)×C41
FittingC2×C3×C41×C49C3
socle, prime radicalC2×C3×C7×C41ΓL(1,𝔽8)
cosocleC3×C49C2×C3×C41
LCSG ▷ C49
UCSC1 ◁ C2×C3×C41

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36162

Conjugacy classes & character table

4674 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36162, 5);