Finite Group Databasebeta

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D29×C7⋊(C52⋊C3) #44478571

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

Aliases

direct productD29×C7⋊(C52⋊C3)
unambiguous semidirect productC29⋊(C2×C7⋊(C52⋊C3))
unambiguous semidirect product(C7×D29)⋊(C52⋊C3)
unambiguous semidirect product(C52×D29)⋊ΓL(1,𝔽8)

Splittings

Fitting, socle, derived, HallC52×C7×C29 ⋊ C2×C3
HallC29×C7⋊(C52⋊C3) ⋊ C2
HallC52×C7×D29 ⋊ C3
HallC52×D29 ⋊ ΓL(1,𝔽8)
HallC52×C29 ⋊ C2×ΓL(1,𝔽8)
HallC7×D29 ⋊ C52⋊C3
HallC7×C29 ⋊ C2×C52⋊C3
HallC52×C7 ⋊ C3×D29
SylowC29 ⋊ C2×C7⋊(C52⋊C3)
SylowC52 ⋊ ΓL(1,𝔽8)×D29
SylowC7 ⋊ D29×C52⋊C3

Subgroups

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

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3045

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 55);