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C3⋊(C5⋊D5)×C29⋊C7 #44478566

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

Aliases

direct productC3⋊(C5⋊D5)×C29⋊C7
unambiguous semidirect productC3⋊(C5⋊D5×C29⋊C7)
unambiguous semidirect productC5⋊(D15×C29⋊C7)
unambiguous semidirect product(C29×C3⋊(C5⋊D5))⋊C7

Splittings

Fitting, socle, derived, HallC3×C52×C29 ⋊ C2×C7
HallC3×C52×C29⋊C7 ⋊ C2
HallC52×C29⋊C7 ⋊ D3
HallC29×C3⋊(C5⋊D5) ⋊ C7
HallC52×C29 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ C5⋊D5
HallC3×C29 ⋊ C7×C5⋊D5
HallC3×C52 ⋊ C2×C29⋊C7
SylowC29 ⋊ C7×C3⋊(C5⋊D5)
SylowC52 ⋊ D3×C29⋊C7
SylowC3 ⋊ C5⋊D5×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C29C2×C7
LCSG ▷ C3×C52×C29
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2175

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 50);