Finite Group Databasebeta

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#32004372

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC71 ⋊ #21557

Subgroups

subgroupG/H
centerC22C2×#14556100
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC4×AGL(1,ℤ/8)×C71C2
socleC22×C71C2×#121
prime radicalC2×AGL(1,ℤ/8)×C71C22
cosocleC22×C4×C71C24
hypercenterC4×AGL(1,ℤ/8)D71
hypocenterC71#21557
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Polycyclic presentation:

2^8,71|a^2=g,b^2=eh,d^2=g,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=dh,i^b=i^70,f^c=fh

Conjugacy classes & character table

1598 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 176488);