Finite Group Databasebeta

C2×#11727714 #13352988

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

Aliases

direct productC2×#11727714

Splittings

FittingC22×C7×C22⋊C8 ⋊ C2
SylowC7 ⋊ C2×#1788

Subgroups

subgroupG/H
centerC24C2×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC22×C7×C22⋊C8C2
socleC24×C7C2×D4
prime radicalC23×#1157C2
cosocleC22×C4×C7C24
hypercenterC22×C22⋊C8D7
hypocenterC7C2×#1788
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

4070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 168760);