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(C5⋊D5)⋊C3×C29⋊C7 #44478554

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

Aliases

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

Splittings

Fitting, socle, derived, HallC52×C29 ⋊ C2×C3×C7
HallC52⋊C3×C29⋊C7 ⋊ C2
HallC5⋊D5×C29⋊C7 ⋊ C3
HallC52×C29⋊C7 ⋊ C2×C3
HallC29×(C5⋊D5)⋊C3 ⋊ C7
HallC29×C52⋊C3 ⋊ C2×C7
HallC29×C5⋊D5 ⋊ C3×C7
HallC52⋊C3 ⋊ C2×C29⋊C7
HallC5⋊D5 ⋊ C3×C29⋊C7
SylowC29 ⋊ C7×(C5⋊D5)⋊C3
SylowC52 ⋊ C2×C3×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C29C2×C3×C7
LCSG ▷ C52×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 435

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 38);