Finite Group Databasebeta

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C29×#1043⋊C9 #39907903

order26100
automorphism?
homologyAbelianization (H1) = C4×C9×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×#1043⋊C9
unambiguous semidirect product#1043⋊(C9×C29)
unambiguous semidirect product(C29×#1043)⋊C9

Splittings

derived, SylowC52 ⋊ C4×C9×C29
HallC29×C52⋊C9 ⋊ C4
HallC29×#1043 ⋊ C9
HallC52×C29 ⋊ C4×C9
HallC52⋊C9 ⋊ C4×C29
Hall#1043 ⋊ C9×C29

Subgroups

subgroupG/H
center, hypercenterC3×C29#1043⋊C3
commutator, hypocenterC52C4×C9×C29
FrattiniC3C29×#1043⋊C3
Fitting, socleC3×C52×C29C3×C4
prime radicalC3×C29×C5⋊D5C2×C3
cosocleC3×C5⋊D5C2×C3×C29
LCSG ▷ C52
UCSC1 ◁ C3×C29

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1305

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 137);