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C4⋊C4×D1028 #45667223

order32896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×D1028

Splittings

FittingC4×C4⋊C4×C257 ⋊ C2
SylowC257 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D257
commutatorC22×C257C23×C4
FittingC4×C4⋊C4×C257C2
socle, cosocleC23×C257C24
prime radicalC22×D1028C22
hypercenterC4×C4⋊C4D257
hypocenterC257D4×C4⋊C4
LCSG ▷ C22×C257 ▷ C257
UCSC1 ◁ C23 ◁ C4×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16448

Conjugacy classes & character table

5170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 7413);