Finite Group Databasebeta

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C2×C5×C17×C37⋊C3 #34038261

order18870
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC2×C5×C17×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C3×C5×C17
HallC5×C17×C37 ⋊ C2×C3
HallC2×C17×C37 ⋊ C3×C5
HallC17×C37 ⋊ C2×C3×C5
HallC2×C5×C37 ⋊ C3×C17
HallC5×C37 ⋊ C2×C3×C17
HallC2×C37 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17C37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C5×C17×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6290

Conjugacy classes & character table

2550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C17×C37⋊C3, C5×C17×Dic37⋊C3, C5×Dic17×C37⋊C3, …
maximal normal subgroup ofC4×C5×C17×C37⋊C3, C5×C17×Dic37⋊C3, C5×Dic17×C37⋊C3, …
maximal quotient ofC4×C5×C17×C37⋊C3, C22×C5×C17×C37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 2);