Finite Group Databasebeta

C2×D7×Q8⋊C8 #13320140

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D7×Q8⋊C8

Splittings

FittingC2×C7×Q8⋊C8 ⋊ C2
SylowC7 ⋊ C22×Q8⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D7
commutatorC4×C7C23×C8
FrattiniC42C23×D7
FittingC2×C7×Q8⋊C8C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC42×C7C24
hypercenterC2×Q8⋊C8D7
hypocenterC7C22×Q8⋊C8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 135912);