Finite Group Databasebeta

#560×Dic43 #25259285

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#560×Dic43

Splittings

SylowC43 ⋊ C4×#560

Subgroups

subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
Fitting, prime radicalC2×C43×#560C2
socle, cosocleC23×C43C25
hypercenterC2×#560D43
hypocenterC43C4×#560
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#560

2568 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 332256);