Finite Group Databasebeta

C7×Dic7⋊C8 #13096091

order1568
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C2

Aliases

direct productC7×Dic7⋊C8
unambiguous semidirect productDic7⋊(C7×C8)

Splittings

SylowC72 ⋊ C4⋊C8

Subgroups

subgroupG/H
centerC2×C4×C7C2×D7
commutatorC2×C7C2×C7×C8
FrattiniC2×C4C2×C7×D7
FittingC2×C72×C8C2
socle, prime radicalC22×C72C2×C4
cosocleC2×C4×C7C22×C7
hypercenterC2×C7×C8D7
hypocenterC7C7×C4⋊C8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4×C7 ◁ C2×C7×C8

109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1568, 257);