Finite Group Databasebeta

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C3×C4×C29×C52⋊C3 #39908003

order26100
automorphism?
homologyAbelianization (H1) = C32×C4×C29 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C4×C29×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C32×C29)
unambiguous semidirect product(C3×C4×C52)⋊(C3×C29)
unambiguous semidirect product(C4×C52×C29)⋊C32
unambiguous semidirect product(C3×C4×C52×C29)⋊C3

Splittings

FittingC3×C4×C52×C29 ⋊ C3
derived, SylowC52 ⋊ C32×C4×C29
HallC4×C52×C29 ⋊ C32
HallC52×C29 ⋊ C32×C4
HallC4×C52 ⋊ C32×C29

Subgroups

subgroupG/H
center, hypercenterC3×C4×C29C52⋊C3
commutator, hypocenterC52C32×C4×C29
FrattiniC2C2×C3×C29×C52⋊C3
FittingC3×C4×C52×C29C3
socleC2×C3×C52×C29C2×C3
prime radicalC2×C3×C29×C52⋊C3C2
cosocleC2×C52C2×C32×C29
LCSG ▷ C52
UCSC1 ◁ C3×C4×C29

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5220

Conjugacy classes & character table

3828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 237);