Finite Group Databasebeta

C2×#22549706 #30640522

order16256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#22549706

Splittings

SylowC127 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D1016
commutatorC8×C127C22×C4
FrattiniC2×C8C22×D127
FittingC22×C16×C127C2
socleC22×C127#107
prime radicalC23×C127Q16
cosocleC2×C8×C127C23
hypercenterC22×C16D127
hypocenterC127C2×#368
LCSG ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 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, 6302);