Finite Group Databasebeta

C4×#16861229 #30647500

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

Aliases

direct productC4×#16861229

Splittings

FittingC4×#41×C127 ⋊ C2
SylowC127 ⋊ C4×#135

Subgroups

subgroupG/H
centerC42C22⋊D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
FittingC4×#41×C127C2
socleC22×C127C22×D4
prime radicalC2×#16861229C2
cosocleC2×C4×C127C24
hypercenterC4×#41D127
hypocenterC127C4×#135
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#41

500 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, 13280);