Finite Group Databasebeta

Q8×#13093938 #26232824

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ8×#13093938

Splittings

FittingQ8×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ Q8×#99

Subgroups

subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingQ8×C22⋊C4×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×C22⋊D47C23
cosocleC24×C47C24
hypercenterQ8×C22⋊C4D47
hypocenterC47Q8×#99
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×Q8 ◁ Q8×C22⋊C4

1354 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 186114);