Finite Group Databasebeta

#360×Dic43 #25011847

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#360×Dic43

Splittings

SylowC43 ⋊ C4×#360

Subgroups

subgroupG/H
centerC22#102×D43
commutatorC8×C43C2×C42
FrattiniC22×C8C22×D43
FittingC2×C43×#360C2
socleC22×C43C2×#102
prime radicalC2×#135×C43C22
cosocleC22×C8×C43C23
hypercenterC2×#360D43
hypocenterC43C4×#360
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

466 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84818);