Finite Group Databasebeta

C2×Q8×#13097544 #38763587

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

Aliases

direct productC2×Q8×#13097544
unambiguous semidirect productD397⋊(C4×Q8)

Splittings

FittingC2×Q8×C397 ⋊ C4
SylowC397 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#13097544
commutatorC2×C397C23×C4
FrattiniC2C23×#13097544
FittingC2×Q8×C397C4
socleC22×C397C22×C4
prime radicalC22×D397C23
cosocleC2×D397C24
hypercenterC2×Q8#13097544
hypocenterC397C2×C4×Q8
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

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, 1614);