Finite Group Databasebeta

C2×C16×D172 #25249748

order11008
isoclinismisoclinic class of Dic86
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×C16×D172

Splittings

FittingC2×C4×C16×C43 ⋊ C2
SylowC43 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C16C2×D43
commutatorC2×C43C23×C16
FrattiniC2×C8C23×D43
FittingC2×C4×C16×C43C2
socleC23×C43C22×C8
prime radicalC22×D172C8
cosocleC2×C8×C43C24
hypercenterC2×C4×C16D43
hypocenterC43C2×D4×C16
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

806 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322719);