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C2×C37×(C31⋊C3)⋊C5 #46806178

order34410
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC2×C37×(C31⋊C3)⋊C5
unambiguous semidirect product(C2×C31⋊C3)⋊(C5×C37)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C3×C37)
unambiguous semidirect product(C2×C37×C31⋊C3)⋊C5

Splittings

Fitting, socle, HallC2×C31×C37 ⋊ C3×C5
derived, SylowC31 ⋊ C2×C3×C5×C37
HallC2×C37×ΓL(1,𝔽32) ⋊ C3
HallC2×C37×C31⋊C3 ⋊ C5
HallC37×ΓL(1,𝔽32) ⋊ C2×C3
HallC37×C31⋊C3 ⋊ C2×C5
HallC31×C37 ⋊ C2×C3×C5
HallC2×ΓL(1,𝔽32) ⋊ C3×C37
HallC2×C31⋊C3 ⋊ C5×C37
HallΓL(1,𝔽32) ⋊ C2×C3×C37
HallC31⋊C3 ⋊ C2×C5×C37
HallC2×C31 ⋊ C3×C5×C37

Subgroups

subgroupG/H
center, hypercenterC2×C37(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C2×C3×C5×C37
FrattiniC1G
Fitting, socleC2×C31×C37C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2294

Conjugacy classes & character table

1258 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34410, 8);