Finite Group Databasebeta

C22×D4×C7⋊C8 #14217628

order1792
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×D4×C7⋊C8

Splittings

SylowC7 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C4C22×D7
commutatorC2×C7C24×C8
FrattiniC2×C4C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C22×C4
prime radicalC23×C7×D4C4
cosocleC2×C4×C7C25
hypercenterC22×C4×D4D7
hypocenterC7C22×C8×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

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, 1033400);