Finite Group Databasebeta

C4×#20263710 #38762375

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

Aliases

direct productC4×#20263710

Splittings

SylowC397 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D397
commutatorC2×C397C2×C42
FrattiniC23C22×D397
FittingC2×C42×C397C2
socle, prime radical, cosocleC23×C397C23
hypercenterC2×C42D397
hypocenterC397C4×C4⋊C4
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25408

Conjugacy classes & character table

6376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 402);