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C2×C61×D31⋊C5 #49180673

order37820
automorphism?
homologyAbelianization (H1) = C22×C5×C61 · Schur multiplier (H2) = C2

Aliases

direct productC2×C61×D31⋊C5
unambiguous semidirect productD31⋊(C2×C5×C61)
unambiguous semidirect product(C2×D31)⋊(C5×C61)
unambiguous semidirect productΓL(1,𝔽32)⋊(C22×C61)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C2×C61)

Splittings

Fitting, socleC2×C31×C61 ⋊ C2×C5
derived, SylowC31 ⋊ C22×C5×C61
HallC61×ΓL(1,𝔽32) ⋊ C22
HallC2×C61×D31 ⋊ C5
HallC31×C61 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C22×C61
HallC2×D31 ⋊ C5×C61

Subgroups

subgroupG/H
center, hypercenterC2×C61D31⋊C5
commutator, cosocle, hypocenterC31C22×C5×C61
FrattiniC1G
Fitting, socleC2×C31×C61C2×C5
LCSG ▷ C31
UCSC1 ◁ C2×C61

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3782

Conjugacy classes & character table

1586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37820, 53);