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AGL(1,ℤ/8)×C7⋊C8 #13323212

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×C7⋊C8

Splittings

SylowC7 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D7
commutatorC4×C7C23×C8
FrattiniC42C23×D7
FittingC4×C7×AGL(1,ℤ/8)C2
socleC22×C7C2×C4×D4
prime radicalC2×C7×AGL(1,ℤ/8)C4
cosocleC42×C7C24
hypercenterC4×AGL(1,ℤ/8)D7
hypocenterC7C8×AGL(1,ℤ/8)
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 138984);