Finite Group Databasebeta

#556×Dic43 #25256554

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

Aliases

direct product#556×Dic43

Splittings

SylowC43 ⋊ C4×#556

Subgroups

subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC2×C43×#556C2
socle, cosocleC23×C43C25
prime radicalC22×D4×C43C23
hypercenterC2×#556D43
hypocenterC43C4×#556
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#556

2340 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 329525);