Finite Group Databasebeta

D8×C22⋊Dic47 #26232102

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD8×C22⋊Dic47

Splittings

SylowC47 ⋊ C22⋊C4×D8

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC23×D8×C47C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC23×D8D47
hypocenterC47C22⋊C4×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

1830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 185392);