Finite Group Databasebeta

C2×#11725830 #13323183

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11725830

Splittings

FittingC2×C7×#322 ⋊ C2
SylowC7 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D28
commutatorC4×C7C23×C8
FrattiniC42C23×D7
FittingC2×C7×#322C2
socleC23×C7C4×D4
prime radicalC22×D28C2×C4
cosocleC42×C7C24
hypercenterC2×#322D7
hypocenterC7C2×SD16⋊C8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#322

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 138955);