Finite Group Databasebeta

← Prev (#50304290) Next (#50304292) →

C2×C5⋊#16838470 #50304291

order38220
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#16838470
unambiguous semidirect product(C2×C5)⋊#16838470

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2×C3
derived, HallC5×C72×C13 ⋊ C22×C3
HallC2×C13×C5⋊(C7⋊D7) ⋊ C3
HallC5×C7×#63270 ⋊ C22
HallC7×#63270 ⋊ C2×D5
HallC2×C5⋊(C7⋊D7) ⋊ C13⋊C3
HallC72×C13 ⋊ C2×C3×D5
HallC5×C72 ⋊ C22×C13⋊C3
HallC5×C13 ⋊ C2×ΓL(1,𝔽8)⋊D7
SylowC72 ⋊ C2×D5×C13⋊C3
SylowC13 ⋊ C2×C5⋊(ΓL(1,𝔽8)⋊D7)
SylowC5 ⋊ C2×#16838470

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#16838470
commutator, cosocle, hypocenterC5×C72×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

200 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 49 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

1176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 977);