Finite Group Databasebeta

C42×Q8×D7 #13511990

order1792
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC42×Q8×D7

Splittings

FittingC42×C7×Q8 ⋊ C2
SylowC7 ⋊ C2×C42×Q8

Subgroups

subgroupG/H
centerC2×C42C22×D7
commutatorC2×C7C23×C42
FrattiniC23C24×D7
FittingC42×C7×Q8C2
socle, cosocleC23×C7C25
prime radicalC23×D7C24
hypercenterC42×Q8D7
hypocenterC7C2×C42×Q8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C42 ◁ C42×Q8

3966 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, 327762);