Finite Group Databasebeta

Q32×D409 #39909673

order26176
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D409

Splittings

FittingQ32×C409 ⋊ C2
SylowC409 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D409
commutator, cosocleC8×C409C23
FrattiniC8C22×D409
FittingQ32×C409C2
socleC2×C409C2×D8
prime radicalC2×D409D8
hypercenterQ32D409
hypocenterC409C2×Q32
LCSG ▷ C8×C409 ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

2266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 975);