Finite Group Databasebeta

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C52×(C19⋊C3)⋊D7 #34093021

order19950
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×(C19⋊C3)⋊D7
unambiguous semidirect product(C19⋊C3)⋊(C52×D7)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C52
HallC52×C7×C19⋊C3 ⋊ C2
HallC52×D133 ⋊ C3
HallC52×C19⋊C3 ⋊ D7
HallC52×C19 ⋊ C3×D7
HallC7×C19⋊C3 ⋊ C2×C52
HallD133 ⋊ C3×C52
HallC52×C7 ⋊ D19⋊C3
HallC19⋊C3 ⋊ C52×D7
SylowC19 ⋊ C3×C52×D7
SylowC7 ⋊ C52×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC52(C19⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C19C2×C3×C52
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3325

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 60);