Finite Group Databasebeta

#410×D127 #30647184

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#410×D127

Splittings

Fitting#410×C127 ⋊ C2
SylowC127 ⋊ C2×#410

Subgroups

subgroupG/H
centerC4C22⋊C4×D127
commutatorC22×C127C23×C4
FrattiniC23C23×D127
Fitting#410×C127C2
socleC2×C127C22×C22⋊C4
prime radicalC2×#41×D127C2
cosocleC23×C127C24
hypercenter#410D127
hypocenterC127C2×#410
LCSG ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

788 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, 12964);