Finite Group Databasebeta

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C2×#22549733 #30641100

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22549733

Splittings

FittingC22×C4⋊C4×C127 ⋊ C2
SylowC127 ⋊ C2×#380

Subgroups

subgroupG/H
centerC24C22×D127
commutatorC22×C127C23×C4
FrattiniC23C23×D127
FittingC22×C4⋊C4×C127C2
socleC24×C127C23
prime radicalC24×D127C22
cosocleC23×C127C24
hypercenterC22×C4⋊C4D127
hypocenterC127C2×#380
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C24 ◁ C22×C4⋊C4

1232 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, 6880);