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C37×Dic261 #50311121

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

Aliases

direct productC37×Dic261
unambiguous semidirect productC9⋊(C37×Dic29)

Splittings

derived, HallC9×C29 ⋊ C4×C37
HallC9×C29×C37 ⋊ C4
HallC29×C37 ⋊ Dic9
HallC9×C37 ⋊ Dic29
SylowC29 ⋊ Dic9×C37
SylowC9 ⋊ C37×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C37D261
commutator, hypocenterC9×C29C4×C37
FrattiniC2×C3C37×D87
FittingC2×C9×C29×C37C2
socle, prime radicalC2×C3×C29×C37D3
cosocleC2×C9×C29C2×C37
LCSG ▷ C9×C29
UCSC1 ◁ C2×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38628

Conjugacy classes & character table

9768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38628, 8);