Finite Group Databasebeta

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C2×#22549901 #30647287

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

Aliases

direct productC2×#22549901

Splittings

FittingC2×C4⋊C8×C127 ⋊ C2
SylowC127 ⋊ C2×#424

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC22×C127C23×C4
FrattiniC2×C4C23×D127
FittingC2×C4⋊C8×C127C2
socleC23×C127C22×C4
prime radicalC23×D127C2×C4
cosocleC2×C4×C127C24
hypercenterC2×C4⋊C8D127
hypocenterC127C2×#424
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

512 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, 13067);