Finite Group Databasebeta

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D37×(C31⋊C3)⋊C5 #46806232

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

Aliases

direct productD37×(C31⋊C3)⋊C5
unambiguous semidirect product(D37×C31⋊C3)⋊C5

Splittings

Fitting, socle, derived, HallC31×C37 ⋊ C2×C3×C5
HallC37×(C31⋊C3)⋊C5 ⋊ C2
HallD37×ΓL(1,𝔽32) ⋊ C3
HallD37×C31⋊C3 ⋊ C5
HallC37×ΓL(1,𝔽32) ⋊ C2×C3
HallC37×C31⋊C3 ⋊ C2×C5
HallC31×D37 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ C3×D37
HallC31⋊C3 ⋊ C5×D37
SylowC37 ⋊ C2×(C31⋊C3)⋊C5
SylowC31 ⋊ C3×C5×D37

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC31×C37C2×C3×C5
LCSG ▷ C31×C37
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1147

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34410, 62);