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C2×C37×C49⋊C9 #45657235

order32634
automorphism?
homologyAbelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC2×C37×C49⋊C9
unambiguous semidirect product(C2×C49)⋊(C9×C37)

Splittings

derived, SylowC49 ⋊ C2×C9×C37
HallC2×C37×C49 ⋊ C9
HallC37×C49 ⋊ C2×C9
HallC2×C49 ⋊ C9×C37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C37C49⋊C3
commutator, hypocenterC49C2×C9×C37
FrattiniC3×C7C2×ΓL(1,𝔽8)×C37
FittingC2×C3×C37×C49C3
socle, prime radicalC2×C3×C7×C37ΓL(1,𝔽8)
cosocleC3×C49C2×C3×C37
LCSG ▷ C49
UCSC1 ◁ C2×C3×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32634

Conjugacy classes & character table

4218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32634, 15);