Finite Group Databasebeta

C16×Dic74 #17996499

order4736
isoclinismisoclinic class of Dic74
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC16×Dic74

Splittings

SylowC37 ⋊ Q8×C16

Subgroups

subgroupG/H
centerC2×C16C2×D37
commutatorC2×C37C22×C16
FrattiniC2×C8C22×D37
FittingC4×C16×C37C2
socle, prime radicalC22×C37C22×C8
cosocleC2×C8×C37C23
hypercenterC4×C16D37
hypocenterC37Q8×C16
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C16 ◁ C4×C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6413);