Finite Group Databasebeta

C2×#27163170 #38763577

order25408
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27163170

Splittings

SylowC397 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#13097544
commutatorC2×C397C22×C8
FrattiniC4C22×#13097544
FittingC22×C4×C397C4
socleC22×C397C2×C8
prime radicalC23×C397C8
cosocle#15691787C23
hypercenterC22×C4#13097544
hypocenterC397C2×M32
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C22×C4

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1604);