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C2×C3⋊D3×AGL(1,𝔽13) #72241859

order5616
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C3⋊D3×AGL(1,𝔽13)

Splittings

Fitting, socleC2×C32×C13 ⋊ C2×C3×C4
derivedC32×C13 ⋊ C22×C3×C4
HallC32×C13⋊C3 ⋊ C22×C4
SylowC13 ⋊ C2×C3×C4×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC2C3⋊D3×AGL(1,𝔽13)
commutator, hypocenterC32×C13C22×C3×C4
FrattiniC1G
Fitting, socleC2×C32×C13C2×C3×C4
prime radicalC2×C3⋊D3×D13⋊C3C2
cosocleC32×D13C23×C3
LCSG ▷ C32×C13
UCSC1 ◁ C2

776 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 776 conjugacy classes of subgroups — too many to draw. Only its 149 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) = 234

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C3⋊D3×AGL(1,𝔽13), #624×AGL(1,𝔽13), C2×D32×AGL(1,𝔽13), …
maximal normal subgroup ofC22×C3⋊D3×AGL(1,𝔽13), #624×AGL(1,𝔽13), C2×D32×AGL(1,𝔽13), …
maximal quotient ofC22×C3⋊D3×AGL(1,𝔽13), D3×C3⋊D3×AGL(1,𝔽13)

GAP

Past the SmallGroups library coverage — no SmallGroups id.