Finite Group Databasebeta

C2×M16×C22⋊D43 #25960496

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×M16×C22⋊D43

Splittings

FittingC23×M16×C43 ⋊ C2
SylowC43 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC23×M16×C43C2
socleC23×C43C23×C4
prime radicalC23×C22⋊D43C4
cosocleC2×C4×C43C25
hypercenterC23×M16D43
hypocenterC43C2×D4×M16
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×M16

3218 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033467);