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AGL(1,ℤ/8)×#3866 #18011351

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#3866

Splittings

FittingAGL(1,ℤ/8)×C37 ⋊ C4
SylowC37 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#3866
commutatorC4×C37C23×C4
FrattiniC4C23×#3866
FittingAGL(1,ℤ/8)×C37C4
socleC2×C37C2×C4×D4
prime radicalAGL(1,ℤ/8)×D37C2
cosocleC4×D37C24
hypercenterAGL(1,ℤ/8)#3866
hypocenterC37C4×AGL(1,ℤ/8)
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 296

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 21265);