Finite Group Databasebeta

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#30597192

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

SylowC61 ⋊ #8092

Subgroups

subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8092
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Polycyclic presentation:

2^8,61|a^2=e,b^2=f,c^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,i^a=i^50,d^b=dh,i^b=i^11,i^e=i^60,i^f=i^60

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1086747);