Finite Group Databasebeta

C8×(C2×D7)⋊C8 #13244262

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC8×(C2×D7)⋊C8

Splittings

FittingC2×C7×C82 ⋊ C2
SylowC7 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
centerC2×C4×C8C2×D7
commutatorC2×C7C2×C82
FrattiniC2×C42C22×D7
FittingC2×C7×C82C2
socleC23×C7C2×C42
prime radicalC23×D7C42
cosocleC2×C42×C7C23
hypercenterC2×C82D7
hypocenterC7C8×C22⋊C8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4×C8 ◁ C2×C82

726 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, 60034);