Finite Group Databasebeta

#576×Dic43 #25960819

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#576×Dic43

Splittings

SylowC43 ⋊ C4×#576

Subgroups

subgroupG/H
centerC22C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
Fitting, prime radicalC2×C43×#576C2
socleC22×C43C23×D4
cosocleC2×C4×C43C25
hypercenterC2×#576D43
hypocenterC43C4×#576
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#576

2826 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, 1033790);