Finite Group Databasebeta

C4×C4⋊#13097544 #38763461

order25408
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊#13097544

Splittings

FittingC42×C397 ⋊ C4
SylowC397 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC2×C4C2×#13097544
commutatorC2×C397C2×C42
FrattiniC22C22×#13097544
FittingC42×C397C4
socleC22×C397C22×C4
prime radical, cosocleC22×D397C23
hypercenterC42#13097544
hypocenterC397C4×C4⋊C4
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1488);