Finite Group Databasebeta

C22×D7×C22⋊C8 #14217221

order1792
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC22×D7×C22⋊C8

Splittings

FittingC22×C7×C22⋊C8 ⋊ C2
SylowC7 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C22×D7
commutatorC2×C7C24×C8
FrattiniC2×C4C24×D7
FittingC22×C7×C22⋊C8C2
socleC24×C7C22×C4
prime radicalC25×D7C4
cosocleC2×C4×C7C25
hypercenterC22×C22⋊C8D7
hypocenterC7C23×C22⋊C8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1032993);