Finite Group Databasebeta

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C2×#13094714 #72245661

order3024
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×#13094714

Splittings

HallC32×ΓL(1,𝔽8) ⋊ C2×D4
SylowC7 ⋊ C2×C3×#638

Subgroups

subgroupG/H
center, hypercenterC22C3⋊D3×AGL(1,𝔽7)
commutator, cosocleC2×C32×C7C23×C3
FrattiniC2C2×C3⋊D3×AGL(1,𝔽7)
Fitting, socleC22×C32×C7C22×C3
hypocenterC32×C7C2×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22

904 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72245533, C2×AGL(1,𝔽7)×#638, C2×C3⋊D3×(C22⋊D7)⋊C3, …
maximal normal subgroup ofC2×#72245533, C2×AGL(1,𝔽7)×#638, C2×C3⋊D3×(C22⋊D7)⋊C3, …
maximal quotient of#72246463, #72254444, #72269433

GAP

Past the SmallGroups library coverage — no SmallGroups id.