Finite Group Databasebeta

C3×C7×D4×D7 #72246492

order2352
automorphism?
homologyAbelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C23

Aliases

direct productC3×C7×D4×D7

Splittings

FittingC3×C72×D4 ⋊ C2
HallC3×C72 ⋊ C2×D4
SylowC72 ⋊ C2×C3×D4

Subgroups

subgroupG/H
centerC2×C3×C7C22×D7
commutator, cosocleC2×C7C23×C3×C7
FrattiniC2C22×C3×C7×D7
FittingC3×C72×D4C2
socleC2×C3×C72C23
hypercenterC3×C7×D4D7
hypocenterC7C2×C3×C7×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3×C7 ◁ C3×C7×D4

264 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 168

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D4×D72, D3×C7×D4×D7, D4×D7×D21, …
maximal normal subgroup ofC3×D4×D72, D3×C7×D4×D7, D4×D7×D21, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.