Finite Group Databasebeta

Q8×#13093939 #26232827

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

Aliases

direct productQ8×#13093939

Splittings

SylowC47 ⋊ Q8×#99

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×D4×Q8×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×C47C23
cosocleC24×C47C24
hypercenterC2×D4×Q8D47
hypocenterC47Q8×#99
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C2×D4×Q8

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, 186117);