Finite Group Databasebeta

C2×#27163103 #38763285

order25408
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27163103

Splittings

SylowC397 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D397
commutatorC2×C397C23×C4
FrattiniC4C23×D397
Fitting, prime radicalC2×#41×C397C2
socleC22×C397C22×C4
cosocleC4×C397C24
hypercenterC2×#41D397
hypocenterC397C2×#131
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1312);