Finite Group Databasebeta

Q16×D761 #37566916

order24352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ16×D761

Splittings

FittingQ16×C761 ⋊ C2
SylowC761 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC2D4×D761
commutator, cosocleC4×C761C23
FrattiniC4C22×D761
FittingQ16×C761C2
socleC2×C761C2×D4
prime radicalC2×D761D4
hypercenterQ16D761
hypocenterC761C2×Q16
LCSG ▷ C4×C761 ▷ C2×C761 ▷ C761
UCSC1 ◁ C2 ◁ C4 ◁ Q16

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12176

Conjugacy classes & character table

2674 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24352, 162);