Finite Group Databasebeta

C2×#27163184 #38763599

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

Aliases

direct productC2×#27163184

Splittings

SylowC397 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#13097544
commutatorC2×C397C23×C4
FrattiniC2C23×#13097544
FittingC2×Q8×C397C4
socleC22×C397C22×C4
prime radicalC2×#20263732C2
cosocleDic397C24
hypercenterC2×Q8#13097544
hypocenterC397C2×#131
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

1030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1626);