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#30616286

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

No aliases for this group.

Splittings

FittingC2×AGL(1,ℤ/8)×C61 ⋊ C4
SylowC61 ⋊ #21235

Subgroups

subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×AGL(1,ℤ/8)×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×D61C2
cosocleC2×C4×D61C24
hypercenterC2×AGL(1,ℤ/8)#6923
hypocenterC61#21235
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Polycyclic presentation:

2^8,61|a^2=g,b^2=egh,c^2=f,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^50,i^b=i^11,d^c=dh,i^g=i^60

Conjugacy classes & character table

394 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1105841);