Finite Group Databasebeta

#26134973

order12032
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingC2×C47×#466 ⋊ C2
SylowC47 ⋊ #13304

Subgroups

subgroupG/H
centerC23C2×#10625334
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC2×C47×#466C2
socleC23×C47C2×D8
hypercenterC2×#466D47
hypocenterC47#13304
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,c^b=cf,d^b=dg,g^b=gh,i^b=i^46

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 88263);