Finite Group Databasebeta

#410×Dic43 #25094250

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#410×Dic43

Splittings

SylowC43 ⋊ C4×#410

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC22×C43C22×C42
FrattiniC24C23×D43
FittingC2×C43×#410C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#41×C43C22
cosocleC24×C43C24
hypercenterC2×#410D43
hypocenterC43C4×#410
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

1666 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, 167221);