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AGL(1,ℤ/8)×#88324 #28316382

order13568
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#88324

Splittings

SylowC53 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×#6157
commutatorC4×C53C23×C8
FrattiniC2×C4C23×#6157
Fitting, prime radicalC2×AGL(1,ℤ/8)×C53C4
socleC22×C53C2×C4×D4
cosocleC4×Dic53C24
hypercenterC2×AGL(1,ℤ/8)#6157
hypocenterC53C8×AGL(1,ℤ/8)
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1101858);