Finite Group Databasebeta

C2×#27163087 #38763043

order25408
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27163087

Splittings

SylowC397 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D397
commutator, cosocleC22×C397C24
FrattiniC22C23×D397
FittingC2×C4⋊C4×C397C2
socle, prime radicalC23×C397C23
hypercenterC2×C4⋊C4D397
hypocenterC397C2×#125
LCSG ▷ C22×C397 ▷ C397
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25408

Conjugacy classes & character table

3988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1070);