Finite Group Databasebeta

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Q8×#13093959 #26235168

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

Aliases

direct productQ8×#13093959

Splittings

SylowC47 ⋊ Q8×#108

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingQ8×M16×C47C2
socleC22×C47C22×C4⋊C4
prime radicalC23×C47C22×Q8
cosocleC22×C4×C47C24
hypercenterQ8×M16D47
hypocenterC47Q8×#108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ Q8×M16

658 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 188458);