Finite Group Databasebeta

C16×#1157 #13507313

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC16×#1157

Splittings

FittingC2×C4×C7×C16 ⋊ C2
SylowC7 ⋊ C16×#41

Subgroups

subgroupG/H
centerC4×C16C2×D7
commutatorC2×C7C23×C16
FrattiniC2×C8C23×D7
FittingC2×C4×C7×C16C2
socleC22×C7C23×C8
prime radicalC2×#1157C8
cosocleC2×C7×C8C24
hypercenterC2×C4×C16D7
hypocenterC7C16×#41
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 323085);