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C7×(C5⋊D5)⋊(C19⋊C3) #34093061

order19950
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×(C5⋊D5)⋊(C19⋊C3)
unambiguous semidirect product(C5⋊D5)⋊(C7×C19⋊C3)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derived, HallC52×C19 ⋊ C2×C3×C7
HallC7×C19⋊(C52⋊C3) ⋊ C2
HallC7×C19×C5⋊D5 ⋊ C3
HallC19⋊(C52⋊C3) ⋊ C2×C7
HallC19×C5⋊D5 ⋊ C3×C7
HallC7×C5⋊D5 ⋊ C19⋊C3
HallC52×C7 ⋊ C2×C19⋊C3
HallC7×C19 ⋊ (C5⋊D5)⋊C3
HallC5⋊D5 ⋊ C7×C19⋊C3
SylowC52 ⋊ C2×C7×C19⋊C3
SylowC19 ⋊ C7×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC7(C5⋊D5)⋊(C19⋊C3)
commutator, cosocle, hypocenterC52×C19C2×C3×C7
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C52×C19
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1995

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 100);