Finite Group Databasebeta

D43×#2138 #25249475

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD43×#2138

Splittings

FittingC43×#2138 ⋊ C2
SylowC43 ⋊ C2×#2138

Subgroups

subgroupG/H
centerC2×C4D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2138C2
socleC22×C43C22×D8
prime radicalC2×#135×D43C2
cosocleC2×C8×C43C24
hypercenter#2138D43
hypocenterC43C2×#2138
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

1190 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, 322446);