Finite Group Databasebeta

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AGL(1,ℤ/8)×Dic197 #38751522

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×Dic197

Splittings

SylowC197 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×D197
commutatorC4×C197C23×C4
FrattiniC2×C4C23×D197
Fitting, prime radicalC2×AGL(1,ℤ/8)×C197C2
socleC22×C197C22×D4
cosocleC2×C4×C197C24
hypercenterC2×AGL(1,ℤ/8)D197
hypocenterC197C4×AGL(1,ℤ/8)
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 13320);