Finite Group Databasebeta

C2×#22549704 #30640510

order16256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#22549704

Splittings

SylowC127 ⋊ C2×#367

Subgroups

subgroupG/H
centerC23D1016
commutatorC8×C127C22×C4
FrattiniC2×C8C22×D127
FittingC22×C16×C127C2
socle, prime radicalC23×C127D8
cosocleC2×C8×C127C23
hypercenterC22×C16D127
hypocenterC127C2×#367
LCSG ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

168 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, 6290);