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C2×C5×C49×D37 #49136389

order36260
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C49×D37
unambiguous semidirect productC37⋊(C22×C5×C49)
unambiguous semidirect product(C2×C37)⋊(C2×C5×C49)

Splittings

FittingC2×C5×C37×C49 ⋊ C2
derived, SylowC37 ⋊ C22×C5×C49
HallC5×C37×C49 ⋊ C22
HallC37×C49 ⋊ C22×C5
HallC5×C37 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C49D37
commutator, hypocenterC37C22×C5×C49
FrattiniC7C2×C5×C7×D37
FittingC2×C5×C37×C49C2
socleC2×C5×C7×C37C2×C7
prime radicalC2×C5×C7×D37C7
cosocleC7×C37C22×C5×C7
LCSG ▷ C37
UCSC1 ◁ C2×C5×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18130

Conjugacy classes & character table

9800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36260, 35);