Finite Group Databasebeta

C2×#11727673 #13319593

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×#11727673

Splittings

FittingC22×C7×C22⋊C8 ⋊ C2
SylowC7 ⋊ C2×#1459

Subgroups

subgroupG/H
centerC22×C4(C2×D7)⋊C4
commutatorC22×C7C23×C8
FrattiniC22×C4C23×D7
FittingC22×C7×C22⋊C8C2
socleC23×C7C2×C22⋊C4
prime radicalC23×C22⋊D7C4
cosocleC22×C4×C7C24
hypercenterC22×C22⋊C8D7
hypocenterC7C2×#1459
LCSG ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

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, 135365);