Finite Group Databasebeta

C2×Dic238 #14274175

order1904
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic238

Splittings

HallC7×C17 ⋊ C2×Q8
SylowC17 ⋊ C2×Dic14
SylowC7 ⋊ C2×Dic34

Subgroups

subgroupG/H
centerC22C2×D119
commutator, cosocleC2×C7×C17C23
FrattiniC2C22×D119
FittingC2×C4×C7×C17C2
socle, prime radicalC22×C7×C17C22
hypercenterC2×C4D119
hypocenterC7×C17C2×Q8
LCSG ▷ C2×C7×C17 ▷ C7×C17
UCSC1 ◁ C22 ◁ C2×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1904, 158);