Finite Group Databasebeta

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C9×C37×Dic29 #50311117

order38628
automorphism?
homologyAbelianization (H1) = C4×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC9×C37×Dic29

Splittings

derived, SylowC29 ⋊ C4×C9×C37
HallC9×C29×C37 ⋊ C4
HallC29×C37 ⋊ C4×C9
HallC9×C29 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC2×C9×C37D29
commutator, hypocenterC29C4×C9×C37
FrattiniC2×C3C3×C37×D29
FittingC2×C9×C29×C37C2
socle, prime radicalC2×C3×C29×C37C2×C3
cosocleC2×C3×C29C2×C3×C37
LCSG ▷ C29
UCSC1 ◁ C2×C9×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38628

Conjugacy classes & character table

10656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38628, 4);