Finite Group Databasebeta

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C4×C29×#66524 #50311115

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

Aliases

direct productC4×C29×#66524

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C4×C29C37⋊C3
commutator, hypocenterC37C4×C9×C29
FrattiniC2×C3C2×C29×C37⋊C3
FittingC3×C4×C29×C37C3
socle, prime radicalC2×C3×C29×C37C2×C3
cosocleC2×C3×C37C2×C3×C29
LCSG ▷ C37
UCSC1 ◁ C3×C4×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38628

Conjugacy classes & character table

5220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38628, 2);