Finite Group Databasebeta

Q32×D397 #38762948

order25408
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D397

Splittings

FittingQ32×C397 ⋊ C2
SylowC397 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D397
commutator, cosocleC8×C397C23
FrattiniC8C22×D397
FittingQ32×C397C2
socleC2×C397C2×D8
prime radicalC2×D397D8
hypercenterQ32D397
hypocenterC397C2×Q32
LCSG ▷ C8×C397 ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 975);