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C22×(C22⋊D127)⋊C4 #30651898

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×(C22⋊D127)⋊C4

Splittings

FittingC22×C22⋊C4×C127 ⋊ C2
SylowC127 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC24C22×D127
commutatorC2×C127C24×C4
FrattiniC22C24×D127
FittingC22×C22⋊C4×C127C2
socleC24×C127C23
prime radicalC23×C22⋊D127C2
cosocleC22×C127C25
hypercenterC22×C22⋊C4D127
hypocenterC127C22×C4×D4
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C24 ◁ C22×C22⋊C4

2528 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, 17678);