Finite Group Databasebeta

C2×#11730857 #13512016

order1792
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#11730857

Splittings

FittingC2×C7×#376 ⋊ C2
SylowC7 ⋊ C2×#2275

Subgroups

subgroupG/H
centerC24C23×D7
commutatorC2×C7C23×C42
FrattiniC23C24×D7
FittingC2×C7×#376C2
socleC24×C7C24
prime radicalC23×D28C22
cosocleC23×C7C25
hypercenterC2×#376D7
hypocenterC7C2×#2275
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#376

4694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 327788);