Finite Group Databasebeta

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C4×#16861187 #30641263

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

Aliases

direct productC4×#16861187

Splittings

FittingC4×C4⋊C4×C127 ⋊ C2
SylowC127 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC22×C127C23×C4
FrattiniC23C23×D127
FittingC4×C4⋊C4×C127C2
socle, cosocleC23×C127C24
prime radicalC23×D127C23
hypercenterC4×C4⋊C4D127
hypocenterC127C4×C22⋊Q8
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

656 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, 7043);