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#14268588⋊C2 #16813428

order3612
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#14268588⋊C2
unambiguous semidirect product#14268592⋊C2
unambiguous semidirect product#14268594⋊C2

Splittings

Fitting, socle, derived, HallC7×C43 ⋊ C22×C3
HallD7×D43 ⋊ C3
Hall#11744749 ⋊ C22
SylowC43 ⋊ C2×AGL(1,𝔽7)
SylowC7 ⋊ C2×D43⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C43C22×C3
LCSG ▷ C7×C43
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 301

Polycyclic presentation:

2^2,3,7,43|e^a=e^42,d^b=d^6,d^c=d^2,e^c=e^36

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D43⋊C3, C3×#14268588⋊C2, #14268588⋊D3, …
maximal normal subgroup ofAGL(1,𝔽7)×D43⋊C3, C3×#14268588⋊C2, C5×#14268588⋊C2, …
maximal quotient of#19129334⋊C2, C3×#14268588⋊C2, #14268588⋊D3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3612, 40);