Finite Group Databasebeta

#421×D127 #30647269

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

Aliases

direct product#421×D127

Splittings

Fitting#421×C127 ⋊ C2
SylowC127 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
Fitting#421×C127C2
socleC2×C127C22×C22⋊C4
prime radicalC2×#41×D127C2
cosocleC2×C4×C127C24
hypercenter#421D127
hypocenterC127C2×#421
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 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, 13049);