Finite Group Databasebeta

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C3×C5⋊(C5⋊(D29⋊C7)) #44478559

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5⋊(C5⋊(D29⋊C7))
unambiguous semidirect productC5⋊(C3×C5⋊(D29⋊C7))
unambiguous semidirect product(C29⋊C7)⋊(C3×C5⋊D5)
unambiguous semidirect product(C3×C5⋊D145)⋊C7

Splittings

Fitting, socle, HallC3×C52×C29 ⋊ C2×C7
derived, HallC52×C29 ⋊ C2×C3×C7
HallC3×C52×C29⋊C7 ⋊ C2
HallC52×C29⋊C7 ⋊ C2×C3
HallC3×C5⋊D145 ⋊ C7
HallC5⋊D145 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ C5⋊D5
HallC29⋊C7 ⋊ C3×C5⋊D5
HallC3×C29 ⋊ C7×C5⋊D5
HallC3×C52 ⋊ D29⋊C7
SylowC29 ⋊ C3×C7×C5⋊D5
SylowC52 ⋊ C3×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C5⋊(D29⋊C7))
commutator, cosocle, hypocenterC52×C29C2×C3×C7
FrattiniC1G
Fitting, socleC3×C52×C29C2×C7
LCSG ▷ C52×C29
UCSC1 ◁ C3

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2175

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 43);