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C4×#17988848 #33092845

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#17988848

Splittings

SylowC73 ⋊ C4×#471

Subgroups

subgroupG/H
centerC2×C4#14556563
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC4×AGL(1,ℤ/8)×C73C2
socleC22×C73C2×#121
prime radicalC2×AGL(1,ℤ/8)×C73C22
cosocleC22×C4×C73C24
hypercenterC4×AGL(1,ℤ/8)D73
hypocenterC73C4×#471
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1648 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 176429);