Finite Group Databasebeta

Q16×D829 #40997481

order26528
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ16×D829

Splittings

FittingQ16×C829 ⋊ C2
SylowC829 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC2D4×D829
commutator, cosocleC4×C829C23
FrattiniC4C22×D829
FittingQ16×C829C2
socleC2×C829C2×D4
prime radicalC2×D829D4
hypercenterQ16D829
hypocenterC829C2×Q16
LCSG ▷ C4×C829 ▷ C2×C829 ▷ C829
UCSC1 ◁ C2 ◁ C4 ◁ Q16

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13264

Conjugacy classes & character table

2912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26528, 162);