Finite Group Databasebeta

← Prev (#35209110) Next (#35209112) →

C2×ΓL(1,𝔽8)×D247 #35209111

order20748
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×ΓL(1,𝔽8)×D247

Splittings

Fitting, socleC2×C7×C13×C19 ⋊ C2×C3
derived, HallC7×C13×C19 ⋊ C22×C3
HallC2×C7×D247 ⋊ C3
HallC13×C19×ΓL(1,𝔽8) ⋊ C22
HallC19×ΓL(1,𝔽8) ⋊ C2×D13
HallC13×ΓL(1,𝔽8) ⋊ C2×D19
HallC13×C19 ⋊ C22×ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×C3×D19
SylowC19 ⋊ C2×ΓL(1,𝔽8)×D13
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D19
SylowC7 ⋊ C2×C3×D247

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×D247
commutator, cosocle, hypocenterC7×C13×C19C22×C3
FrattiniC1G
Fitting, socleC2×C7×C13×C19C2×C3
LCSG ▷ C7×C13×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3458

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 339);