Finite Group Databasebeta

C4×#90270 #13513772

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#90270

Splittings

FittingC42×C7×Q8 ⋊ C2
SylowC7 ⋊ C4×#554

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC42×C7×Q8C2
socle, cosocleC23×C7C25
prime radicalC22×D28C23
hypercenterC42×Q8D7
hypocenterC7C4×#554
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C42×Q8

2516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 329544);