Finite Group Databasebeta

C8×M16×D43 #25062167

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×M16×D43

Splittings

FittingC8×M16×C43 ⋊ C2
SylowC43 ⋊ C2×C8×M16

Subgroups

subgroupG/H
centerC4×C8C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC42C23×D43
FittingC8×M16×C43C2
socleC22×C43C22×C42
prime radicalC23×D43C42
cosocleC42×C43C24
hypercenterC8×M16D43
hypocenterC43C2×C8×M16
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C4×C8 ◁ C8×M16

1046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135138);