Finite Group Databasebeta

D4×Q8×Dic47 #26376146

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×Q8×Dic47

Splittings

SylowC47 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC2×D4×Q8×C47C2
socle, cosocleC23×C47C25
prime radicalC22×D4×C47C23
hypercenterC2×D4×Q8D47
hypocenterC47C4×D4×Q8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×D4×Q8

3148 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 329436);