Finite Group Databasebeta

C2×#22549774 #30641181

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22549774

Splittings

SylowC127 ⋊ C2×#389

Subgroups

subgroupG/H
centerC24C22×D127
commutatorC22×C127C23×C4
FrattiniC23C23×D127
FittingC22×C42×C127C2
socle, prime radicalC24×C127C23
cosocleC23×C127C24
hypercenterC22×C42D127
hypocenterC127C2×#389
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C24 ◁ C22×C42

800 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6961);