Finite Group Databasebeta

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C2×C5×C17×D111 #49179915

order37740
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C17×D111
unambiguous semidirect product(C2×C3)⋊(C5×C17×D37)
unambiguous semidirect product(C2×C37)⋊(C5×D3×C17)

Splittings

Fitting, socleC2×C3×C5×C17×C37 ⋊ C2
derived, HallC3×C37 ⋊ C22×C5×C17
HallC3×C5×C17×C37 ⋊ C22
HallC5×C17×C37 ⋊ C2×D3
HallC3×C17×C37 ⋊ C22×C5
HallC17×C37 ⋊ C2×C5×D3
HallC3×C5×C37 ⋊ C22×C17
HallC3×C5×C17 ⋊ C2×D37
HallC5×C37 ⋊ C2×D3×C17
HallC3×C17 ⋊ C2×C5×D37
SylowC37 ⋊ C2×C5×D3×C17
HallC3×C5 ⋊ C2×C17×D37
SylowC3 ⋊ C2×C5×C17×D37

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17D111
commutator, cosocle, hypocenterC3×C37C22×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C37C2
LCSG ▷ C3×C37
UCSC1 ◁ C2×C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18870

Conjugacy classes & character table

9690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 170);