Finite Group Databasebeta

C2×#11727543 #13351626

order1792
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#11727543

Splittings

FittingC22×C4×C7×C8 ⋊ C2
SylowC7 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC22×C8D28
commutatorC4×C7C22×C42
FrattiniC22×C4C23×D7
FittingC22×C4×C7×C8C2
socleC23×C7C4×D4
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenterC22×C4×C8D7
hypocenterC7C2×#1764
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×C4×C8

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 167398);