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C2×#22625931 #34021622

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22625931
unambiguous semidirect productD73⋊#1883

Splittings

FittingC2×AGL(1,ℤ/8)×C73 ⋊ C4
SylowC73 ⋊ C2×#1883

Subgroups

subgroupG/H
centerC22#17989535
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×AGL(1,ℤ/8)×C73C4
socleC22×C73#386
prime radicalC2×AGL(1,ℤ/8)×D73C2
cosocleC2×C4×D73C24
hypercenterC2×AGL(1,ℤ/8)#64408
hypocenterC73C2×#1883
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

2018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1168

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1105206);