Finite Group Databasebeta

C2×#11727641 #13351628

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

Aliases

direct productC2×#11727641

Splittings

FittingC2×C7×#405 ⋊ C2
SylowC7 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC22×C8C22⋊D7
commutatorC4×C7C22×C42
FrattiniC22×C4C23×D7
FittingC2×C7×#405C2
socleC23×C7C4×D4
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenterC2×#405D7
hypocenterC7C2×#1764
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C2×#405

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

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, 167400);