Finite Group Databasebeta

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C4×C29×#66526 #50311170

order38628
automorphism?
homologyAbelianization (H1) = C4×C9×C29 · Schur multiplier (H2) = C1

Aliases

direct productC4×C29×#66526

Splittings

Fitting, HallC4×C29×C37 ⋊ C9
derived, SylowC37 ⋊ C4×C9×C29
HallC29×C37 ⋊ C4×C9
HallC4×C37 ⋊ C9×C29

Subgroups

subgroupG/H
center, hypercenterC4×C29#66526
commutator, hypocenterC37C4×C9×C29
FrattiniC2C2×C29×#66526
FittingC4×C29×C37C9
socleC2×C29×C37C2×C9
prime radicalC2×C29×C37⋊C3C2×C3
cosocleC2×C37⋊C3C2×C3×C29
LCSG ▷ C37
UCSC1 ◁ C4×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4292

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38628, 57);