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C2×C52⋊C3×C29⋊C7 #44478555

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

Aliases

direct productC2×C52⋊C3×C29⋊C7
unambiguous semidirect product(C2×C52)⋊(C3×C29⋊C7)
unambiguous semidirect product(C2×C29)⋊(C7×C52⋊C3)
unambiguous semidirect product(C2×C29×C52⋊C3)⋊C7
unambiguous semidirect product(C2×C52×C29⋊C7)⋊C3

Splittings

Fitting, socle, HallC2×C52×C29 ⋊ C3×C7
derived, HallC52×C29 ⋊ C2×C3×C7
HallC2×C52×C29⋊C7 ⋊ C3
HallC52×C29⋊C7 ⋊ C2×C3
HallC2×C29×C52⋊C3 ⋊ C7
HallC29×C52⋊C3 ⋊ C2×C7
HallC2×C29 ⋊ C7×C52⋊C3
HallC2×C52 ⋊ C3×C29⋊C7
SylowC29 ⋊ C2×C7×C52⋊C3
SylowC52 ⋊ C2×C3×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2C52⋊C3×C29⋊C7
commutator, cosocle, hypocenterC52×C29C2×C3×C7
FrattiniC1G
Fitting, socleC2×C52×C29C3×C7
LCSG ▷ C52×C29
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 870

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 39);