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C7×C5⋊(C5⋊(D19⋊C3)) #34093039

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

Aliases

direct productC7×C5⋊(C5⋊(D19⋊C3))
unambiguous semidirect productC5⋊(C7×C5⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C7×C5⋊D5)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derived, HallC52×C19 ⋊ C2×C3×C7
HallC52×C7×C19⋊C3 ⋊ C2
HallC7×C5⋊D95 ⋊ C3
HallC52×C19⋊C3 ⋊ C2×C7
HallC5⋊D95 ⋊ C3×C7
HallC7×C19⋊C3 ⋊ C5⋊D5
HallC52×C7 ⋊ D19⋊C3
HallC7×C19 ⋊ C3×C5⋊D5
HallC19⋊C3 ⋊ C7×C5⋊D5
SylowC52 ⋊ C7×D19⋊C3
SylowC19 ⋊ C3×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC7C5⋊(C5⋊(D19⋊C3))
commutator, cosocle, hypocenterC52×C19C2×C3×C7
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C52×C19
UCSC1 ◁ C7

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3325

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 78);