Finite Group Databasebeta

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C3×C29×C5⋊D35 #44478609

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C5

Aliases

direct productC3×C29×C5⋊D35
unambiguous semidirect productC5⋊(C3×C29×D35)

Splittings

Fitting, socle, HallC3×C52×C7×C29 ⋊ C2
derived, HallC52×C7 ⋊ C2×C3×C29
HallC52×C7×C29 ⋊ C2×C3
HallC3×C52×C29 ⋊ D7
HallC52×C29 ⋊ C3×D7
HallC3×C7×C29 ⋊ C5⋊D5
HallC3×C52×C7 ⋊ C2×C29
HallC7×C29 ⋊ C3×C5⋊D5
HallC3×C52 ⋊ D7×C29
SylowC52 ⋊ C3×D7×C29
HallC3×C7 ⋊ C29×C5⋊D5
SylowC7 ⋊ C3×C29×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C29C5⋊D35
commutator, cosocle, hypocenterC52×C7C2×C3×C29
FrattiniC1G
Fitting, socleC3×C52×C7×C29C2
LCSG ▷ C52×C7
UCSC1 ◁ C3×C29

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15225

Conjugacy classes & character table

7743 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 93);