Finite Group Databasebeta

C7×Q8×D17 #14274161

order1904
automorphism?
homologyAbelianization (H1) = C23×C7 · Schur multiplier (H2) = C22

Aliases

direct productC7×Q8×D17

Splittings

FittingC7×Q8×C17 ⋊ C2
HallC7×C17 ⋊ C2×Q8
SylowC17 ⋊ C2×C7×Q8

Subgroups

subgroupG/H
centerC2×C7C22×D17
commutator, cosocleC2×C17C23×C7
FrattiniC2C22×C7×D17
FittingC7×Q8×C17C2
socleC2×C7×C17C23
prime radicalC2×C7×D17C22
hypercenterC7×Q8D17
hypocenterC17C2×C7×Q8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C7 ◁ C7×Q8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1904, 144);