Finite Group Databasebeta

C4×#20263715 #38762475

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

Aliases

direct productC4×#20263715

Splittings

SylowC397 ⋊ C4×M16

Subgroups

subgroupG/H
centerC42C2×D397
commutatorC2×C397C2×C42
FrattiniC2×C4C22×D397
FittingC2×C42×C397C2
socleC22×C397C22×C4
prime radicalC23×C397C2×C4
cosocleC2×C4×C397C23
hypercenterC2×C42D397
hypocenterC397C4×M16
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C42 ◁ C2×C42

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

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, 502);