Finite Group Databasebeta

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C2×D4×C3⋊#64424 #72246381

order14112
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×C3⋊#64424

Splittings

FittingC2×C3×C72×D4 ⋊ C2×C3
HallC3×#3861 ⋊ C22×D4
SylowC72 ⋊ C2×C3×D3×D4

Subgroups

subgroupG/H
centerC22C22×C3⋊#64424
commutator, cosocleC2×C3×C72C24×C3
FrattiniC2C23×C3⋊#64424
FittingC2×C3×C72×D4C2×C3
socleC22×C3×C72C23×C3
hypercenterC2×D4C3⋊#64424
hypocenterC3×C72C22×C3×D4
LCSG ▷ C2×C3×C72 ▷ C3×C72
UCSC1 ◁ C22 ◁ C2×D4

4990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1176

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×D3×D4×#64424
maximal normal subgroup ofC2×D3×D4×#64424

GAP

Past the SmallGroups library coverage — no SmallGroups id.