Finite Group Databasebeta

#26213624

order12032
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #20331

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC2×C47C2×C43
FittingC22×#97×C47C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC22×#97D47
hypocenterC47#20331
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×#97

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=e,b^2=f,c^2=g,e^2=h,c^a=ch,d^b=dh,i^b=i^46

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166914);