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C4×#19098729 #34294139

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#19098729

Splittings

FittingC4×AGL(1,ℤ/8)×C79 ⋊ C2
SylowC79 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2×C4#14579129
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC4×AGL(1,ℤ/8)×C79C2
socleC22×C79C2×#120
prime radicalC2×#19098729C2
cosocleC22×C4×C79C24
hypercenterC4×AGL(1,ℤ/8)D79
hypocenterC79C4×#453
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

1578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2528

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 175438);