Finite Group Databasebeta

C22×#20263710 #38762972

order25408
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#20263710

Splittings

SylowC397 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D397
commutatorC2×C397C23×C4
FrattiniC22C23×D397
FittingC23×C4×C397C2
socle, prime radicalC24×C397C22
cosocleC22×C397C24
hypercenterC23×C4D397
hypocenterC397C22×C4⋊C4
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C24 ◁ C23×C4

418 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, 999);