Finite Group Databasebeta

← Prev (#26013951) Next (#26013953) →

C2×C7×#11716326 #26013952

order11172
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×#11716326

Splittings

Fitting, socleC2×C72×C19 ⋊ C2×C3
derivedC7×C19 ⋊ C22×C3×C7
HallC2×C7×D7×C19 ⋊ C3
HallC7×#87705 ⋊ C22
HallC72×C19 ⋊ C22×C3
HallC2×C7×D7 ⋊ C19⋊C3
SylowC72 ⋊ C22×C19⋊C3
SylowC19 ⋊ C2×C7×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC2×C7#11716326
commutator, cosocle, hypocenterC7×C19C22×C3×C7
FrattiniC1G
Fitting, socleC2×C72×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C7

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

518 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×AGL(1,𝔽7)×C19⋊C3, C2×ΓL(1,𝔽8)×#11716326, C2×#30660683, …
maximal normal subgroup ofC2×C7×AGL(1,𝔽7)×C19⋊C3, C2×ΓL(1,𝔽8)×#11716326, C2×#30660683, …
maximal quotient ofC2×C7×#14558785, D3×C7×#11716326, C2×C3×C7×#11716326, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11172, 214);