Finite Group Databasebeta

C2×C4×Q16×D43 #25960609

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

Aliases

direct productC2×C4×Q16×D43

Splittings

FittingC2×C4×Q16×C43 ⋊ C2
SylowC43 ⋊ C22×C4×Q16

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC2×C4×C43C25
hypercenterC2×C4×Q16D43
hypocenterC43C22×C4×Q16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

2830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033580);