Finite Group Databasebeta

C4×#90242 #13513634

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#90242

Splittings

FittingC42×C7×D4 ⋊ C2
SylowC7 ⋊ C4×#547

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC42×C7×D4C2
socle, cosocleC23×C7C25
prime radicalC2×#90242C2
hypercenterC42×D4D7
hypocenterC7C4×#547
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C42×D4

3268 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, 329406);