Finite Group Databasebeta

#344×Dic43 #25001804

order11008
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#344×Dic43

Splittings

SylowC43 ⋊ C4×#344

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC22×C43C43
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43C2×#95
prime radicalC24×C43C22×C4
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43C4×#344
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

906 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 74775);