Finite Group Databasebeta

SD16×D107 #16812121

order3424
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD16×D107

Splittings

FittingSD16×C107 ⋊ C2
SylowC107 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC2D4×D107
commutator, cosocleC4×C107C23
FrattiniC4C22×D107
FittingSD16×C107C2
socleC2×C107C2×D4
prime radicalD4×D107C2
hypercenterSD16D107
hypocenterC107C2×SD16
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C4 ◁ SD16

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3424, 158);