Finite Group Databasebeta

C22×Dic1016 #30651843

order16256
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1016

Splittings

SylowC127 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23D1016
commutator, cosocleC8×C127C24
FrattiniC8C23×D127
FittingC22×C16×C127C2
socle, prime radicalC23×C127D8
hypercenterC22×C16D127
hypocenterC127C22×Q32
LCSG ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17623);