Finite Group Databasebeta

C22×#16861155 #30651842

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

Aliases

direct productC22×#16861155

Splittings

SylowC127 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23#14523233
commutator, cosocleC8×C127C24
FrattiniC8C23×D127
FittingC22×Q16×C127C2
socle, prime radicalC23×C127D8
hypercenterC22×Q16D127
hypocenterC127C22×Q32
LCSG ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17622);