Finite Group Databasebeta

#344×D127 #30638470

order16256
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#344×D127

Splittings

Fitting#344×C127 ⋊ C2
SylowC127 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D127
commutatorC22×C127C2×C42
FrattiniC22×C4C22×D127
Fitting#344×C127C2
socleC2×C127C2×#95
prime radicalC23×D127C2×C4
cosocleC22×C4×C127C23
hypercenter#344D127
hypocenterC127C2×#344
LCSG ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 4250);