Finite Group Databasebeta

D43×#2158 #25249622

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD43×#2158

Splittings

FittingC43×#2158 ⋊ C2
SylowC43 ⋊ C2×#2158

Subgroups

subgroupG/H
centerC2×C4D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2158C2
socleC22×C43C22×D8
prime radicalC23×D43D8
cosocleC2×C8×C43C24
hypercenter#2158D43
hypocenterC43C2×#2158
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2158

694 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, 322593);