Finite Group Databasebeta

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#30597378

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

SylowC61 ⋊ #8132

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×#6923
commutatorC22×C61C2×C4×C8
FittingC2×C4×C8×C61C4
socle, prime radicalC23×C61C2×C42
cosocleC2×C4×Dic61C23
hypercenterC2×C4×C8#6923
hypocenterC61#8132
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×C8

478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Polycyclic presentation:

2^8,61|a^2=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=cg,i^a=i^11,i^e=i^60

Conjugacy classes & character table

1072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1086933);