Finite Group Databasebeta

Q8×#13093960 #26235171

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productQ8×#13093960

Splittings

SylowC47 ⋊ Q8×#108

Subgroups

subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C8×Q8×C47C2
socleC22×C47C22×C4⋊C4
prime radicalC23×C47C22×Q8
cosocleC22×C4×C47C24
hypercenterC2×C8×Q8D47
hypocenterC47Q8×#108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ C2×C8×Q8

658 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 188461);