Finite Group Databasebeta

#324×Dic43 #24987105

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#324×Dic43

Splittings

SylowC43 ⋊ C4×#324

Subgroups

subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C43C2×C4×C8
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22×C4
cosocleC23×C4×C43C23
hypercenterC2×#324D43
hypocenterC43C4×#324
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

730 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, 60076);