Finite Group Databasebeta

← Prev (#30647278) Next (#30647280) →

C2×C4⋊C8×D127 #30647279

order16256
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C4⋊C8×D127

Splittings

FittingC2×C4⋊C8×C127 ⋊ C2
SylowC127 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC2×C127C23×C8
FrattiniC2×C4C23×D127
FittingC2×C4⋊C8×C127C2
socleC23×C127C22×C4
prime radicalC23×D127C2×C4
cosocleC2×C4×C127C24
hypercenterC2×C4⋊C8D127
hypocenterC127C22×C4⋊C8
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

640 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13059);