Finite Group Databasebeta

C23×#14523232 #30653432

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#14523232

Splittings

SylowC127 ⋊ C23×M16

Subgroups

subgroupG/H
centerC23×C4C2×D127
commutatorC2×C127C24×C4
FrattiniC4C24×D127
FittingC24×C4×C127C2
socleC24×C127C2×C4
prime radicalC25×C127C4
cosocleC4×C127C25
hypercenterC24×C4D127
hypocenterC127C23×M16
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C23×C4 ◁ C24×C4

1720 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 19212);