Finite Group Databasebeta

#576×D127 #30653478

order16256
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#576×D127

Splittings

Fitting#576×C127 ⋊ C2
SylowC127 ⋊ C2×#576

Subgroups

subgroupG/H
centerC2C22×D4×D127
commutator, cosocleC4×C127C25
FrattiniC4C24×D127
Fitting#576×C127C2
socleC2×C127C23×D4
hypercenter#576D127
hypocenterC127C2×#576
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ #41 ◁ #576

1512 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, 19258);