Finite Group Databasebeta

← Prev (#45667234) Next (#45667236) →

C4⋊C4×Dic514 #45667235

order32896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic514

Splittings

SylowC257 ⋊ Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D257
commutatorC22×C257C23×C4
FittingC4×C4⋊C4×C257C2
socle, prime radical, cosocleC23×C257C24
hypercenterC4×C4⋊C4D257
hypocenterC257Q8×C4⋊C4
LCSG ▷ C22×C257 ▷ C257
UCSC1 ◁ C23 ◁ C4×C4⋊C4

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32896

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, 7425);