Finite Group Databasebeta

#322×D127 #30637004

order16256
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#322×D127

Splittings

Fitting#322×C127 ⋊ C2
SylowC127 ⋊ C2×#322

Subgroups

subgroupG/H
center, FrattiniC42C22×D127
commutatorC2×C127C2×C4×C8
Fitting#322×C127C2
socleC22×C127C2×C42
prime radicalC22×D127C42
cosocleC42×C127C23
hypercenter#322D127
hypocenterC127C2×#322
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C42 ◁ #322

248 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 2784);