Finite Group Databasebeta

C4×#16861215 #30647150

order16256
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#16861215

Splittings

FittingC2×C4×C8×C127 ⋊ C2
SylowC127 ⋊ C4×#131

Subgroups

subgroupG/H
centerC4×C8C2×D127
commutatorC2×C127C22×C42
FrattiniC2×C4C23×D127
FittingC2×C4×C8×C127C2
socleC22×C127C23×C4
prime radicalC2×#14523248C22
cosocleC2×C4×C127C24
hypercenterC2×C4×C8D127
hypocenterC127C4×#131
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

572 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, 12930);