Finite Group Databasebeta

#26109347

order12032
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #8647

Subgroups

subgroupG/H
centerC23#13093998
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C8×Q8×C47C2
socle, prime radicalC23×C47#121
cosocleC2×C42×C47C23
hypercenterC2×C8×Q8D47
hypocenterC47#8647
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×Q8

438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=f,b^2=dh,c^2=h,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^46,e^c=eh

Conjugacy classes & character table

1898 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 62637);