Finite Group Databasebeta

← Prev (#37561351) Next (#37561353) →

ΓL(1,𝔽8)×D15×D19 #37561352

order23940
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productΓL(1,𝔽8)×D15×D19

Splittings

Fitting, socle, derivedC3×C5×C7×C19 ⋊ C22×C3
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C22
HallC3×C19×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×C7×C19 ⋊ C2×C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×D19
HallC7×C19 ⋊ C2×C3×D15
HallC5×C19 ⋊ C2×D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D5×D19
HallC5×C7 ⋊ C3×D3×D19
SylowC19 ⋊ C2×ΓL(1,𝔽8)×D15
SylowC7 ⋊ C3×D15×D19
SylowC5 ⋊ D3×ΓL(1,𝔽8)×D19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C19C22×C3
LCSG ▷ C3×C5×C7×C19
UCSC1

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1995

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 484);