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C29×Dic333 #50311120

order38628
automorphism?
homologyAbelianization (H1) = C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×Dic333
unambiguous semidirect productC9⋊(C29×Dic37)

Splittings

derived, HallC9×C37 ⋊ C4×C29
HallC9×C29×C37 ⋊ C4
HallC29×C37 ⋊ Dic9
HallC9×C29 ⋊ Dic37
SylowC37 ⋊ C29×Dic9
SylowC9 ⋊ C29×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C29D333
commutator, hypocenterC9×C37C4×C29
FrattiniC2×C3C29×D111
FittingC2×C9×C29×C37C2
socle, prime radicalC2×C3×C29×C37D3
cosocleC2×C9×C37C2×C29
LCSG ▷ C9×C37
UCSC1 ◁ C2×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38628

Conjugacy classes & character table

9744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38628, 7);