Finite Group Databasebeta

C22×D7×#104 #14217382

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×D7×#104

Splittings

FittingC22×C7×#104 ⋊ C2
SylowC7 ⋊ C23×#104

Subgroups

subgroupG/H
centerC22×C4D4×D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC22×C7×#104C2
socleC23×C7C2×C22⋊C4
prime radicalC22×D7×#41C2
cosocleC2×C4×C7C25
hypercenterC22×#104D7
hypocenterC7C23×#104
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

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, 1033154);