Finite Group Databasebeta

← Prev (#72222009) Next (#72222011) →

D4×ΓL(1,𝔽8)2 #72222010

order3528
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productD4×ΓL(1,𝔽8)2

Splittings

Fitting, HallC72×D4 ⋊ C32
SylowC72 ⋊ C32×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×ΓL(1,𝔽8)2
commutator, socle, cosocleC2×C72C22×C32
FittingC72×D4C32
hypercenterD4ΓL(1,𝔽8)2
hypocenterC72C32×D4
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ D4

224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×ΓL(1,𝔽8)⋊AGL(1,𝔽7), ΓL(1,𝔽8)2×S4, C2×D4×ΓL(1,𝔽8)2, …
maximal normal subgroup ofD4×ΓL(1,𝔽8)⋊AGL(1,𝔽7), C2×D4×ΓL(1,𝔽8)2, #41×ΓL(1,𝔽8)2, …
maximal quotient ofC2×D4×ΓL(1,𝔽8)2, SD16×ΓL(1,𝔽8)2, D8×ΓL(1,𝔽8)2, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.