Finite Group Databasebeta

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C3×C5×D17×C37 #34038263

order18870
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D17×C37
unambiguous semidirect productC17⋊(C2×C3×C5×C37)

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C2
derived, SylowC17 ⋊ C2×C3×C5×C37
HallC5×C17×C37 ⋊ C2×C3
HallC3×C17×C37 ⋊ C2×C5
HallC17×C37 ⋊ C2×C3×C5
HallC3×C5×C17 ⋊ C2×C37
HallC5×C17 ⋊ C2×C3×C37
HallC3×C17 ⋊ C2×C5×C37

Subgroups

subgroupG/H
center, hypercenterC3×C5×C37D17
commutator, cosocle, hypocenterC17C2×C3×C5×C37
FrattiniC1G
Fitting, socleC3×C5×C17×C37C2
LCSG ▷ C17
UCSC1 ◁ C3×C5×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

5550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C37×#595, C3×C5×#14578981, C3×C5×D17×D37, …
maximal normal subgroup ofC3×C5×C37×#595, C3×C5×#14578981, C3×C5×D17×D37, …
maximal quotient ofC3×C5×C37×Dic17, C2×C3×C5×D17×C37

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 4);