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C2×C19×C7⋊(C52⋊C3) #34093096

order19950
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C5

Aliases

direct productC2×C19×C7⋊(C52⋊C3)
unambiguous semidirect product(C2×C7)⋊(C19×C52⋊C3)
unambiguous semidirect product(C2×C52)⋊(C19×ΓL(1,𝔽8))

Splittings

Fitting, socle, HallC2×C52×C7×C19 ⋊ C3
derived, HallC52×C7 ⋊ C2×C3×C19
HallC52×C7×C19 ⋊ C2×C3
HallC2×C52×C19 ⋊ ΓL(1,𝔽8)
HallC52×C19 ⋊ C2×ΓL(1,𝔽8)
HallC2×C52×C7 ⋊ C3×C19
HallC2×C7×C19 ⋊ C52⋊C3
HallC7×C19 ⋊ C2×C52⋊C3
HallC2×C52 ⋊ C19×ΓL(1,𝔽8)
SylowC52 ⋊ C2×C19×ΓL(1,𝔽8)
HallC2×C7 ⋊ C19×C52⋊C3
SylowC7 ⋊ C2×C19×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C19C7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7C2×C3×C19
FrattiniC1G
Fitting, socleC2×C52×C7×C19C3
LCSG ▷ C52×C7
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3990

Conjugacy classes & character table

2318 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 135);