Finite Group Databasebeta

C23×#14523235 #30653448

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

Aliases

direct productC23×#14523235

Splittings

FittingC23×Q8×C127 ⋊ C2
SylowC127 ⋊ C23×SD16

Subgroups

subgroupG/H
centerC24C22⋊D127
commutator, cosocleC4×C127C25
FrattiniC4C24×D127
FittingC23×Q8×C127C2
socleC24×C127D4
prime radicalC23×D508C2
hypercenterC23×Q8D127
hypocenterC127C23×SD16
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q8

1720 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 19228);