Finite Group Databasebeta

← Prev (#50303858) Next (#50303860) →

C7×ΓL(1,𝔽8)⋊#63120 #50303859

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×ΓL(1,𝔽8)⋊#63120
unambiguous semidirect productΓL(1,𝔽8)⋊(C7×#63120)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derivedC5×C7×C13 ⋊ C3×C4×C7
HallC7×C7⋊#63120 ⋊ C3
HallC5×C7×C13×ΓL(1,𝔽8) ⋊ C4
HallC7×C13×ΓL(1,𝔽8) ⋊ AGL(1,𝔽5)
HallC5×C7×ΓL(1,𝔽8) ⋊ Dic13
HallC72×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C72 ⋊ C3×Dic13
HallC7×ΓL(1,𝔽8) ⋊ #63120
HallC5×C13 ⋊ C7×ΓL(1,𝔽8)⋊C4
SylowC72 ⋊ C3×#63120
SylowC13 ⋊ C7×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
SylowC5 ⋊ C7×ΓL(1,𝔽8)⋊Dic13

Subgroups

subgroupG/H
center, hypercenterC7ΓL(1,𝔽8)⋊#63120
commutator, hypocenterC5×C7×C13C3×C4×C7
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC7×D5×C13×ΓL(1,𝔽8)C2
cosocleC7×D5×C13C2×C3×C7
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 2730

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 545);