Finite Group Databasebeta

C2×#11725829 #13319503

order1792
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8

Aliases

direct productC2×#11725829

Splittings

FittingC2×C7×#322 ⋊ C2
SylowC7 ⋊ C2×#1455

Subgroups

subgroupG/H
centerC2×C42C22×D7
commutatorC22×C7C22×C42
FrattiniC42C23×D7
FittingC2×C7×#322C2
socleC23×C7C2×C42
prime radicalC23×D7C42
cosocleC42×C7C24
hypercenterC2×#322D7
hypocenterC7C2×#1455
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C42 ◁ C2×#322

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 135275);