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C4×(C22⋊D127)⋊C4 #30641074

order16256
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×(C22⋊D127)⋊C4

Splittings

FittingC4×C22⋊C4×C127 ⋊ C2
SylowC127 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC2×C127C22×C42
FrattiniC23C23×D127
FittingC4×C22⋊C4×C127C2
socle, cosocleC23×C127C24
prime radicalC22×C22⋊D127C22
hypercenterC4×C22⋊C4D127
hypocenterC127C42×D4
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 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, 6854);