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ΓL(1,𝔽8)×C5⋊D95 #34093052

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

Aliases

direct productΓL(1,𝔽8)×C5⋊D95
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D95)

Splittings

Fitting, socle, derived, HallC52×C7×C19 ⋊ C2×C3
HallC52×C19×ΓL(1,𝔽8) ⋊ C2
HallC7×C5⋊D95 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ D19
HallC52×C19 ⋊ C2×ΓL(1,𝔽8)
HallC19×ΓL(1,𝔽8) ⋊ C5⋊D5
HallC52×C7 ⋊ C3×D19
HallC7×C19 ⋊ C3×C5⋊D5
SylowC52 ⋊ ΓL(1,𝔽8)×D19
SylowC19 ⋊ ΓL(1,𝔽8)×C5⋊D5
SylowC7 ⋊ C3×C5⋊D95

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C19C2×C3
LCSG ▷ C52×C7×C19
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3325

Conjugacy classes & character table

1195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 91);