Finite Group Databasebeta

C22×#16861141 #30647302

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

Aliases

direct productC22×#16861141

Splittings

SylowC127 ⋊ C22×#106

Subgroups

subgroupG/H
centerC24D508
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
FittingC23×C8×C127C2
socle, prime radicalC24×C127D4
cosocleC2×C4×C127C24
hypercenterC23×C8D127
hypocenterC127C22×#106
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 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, 13082);