Finite Group Databasebeta

C4×#89254 #13244389

order1792
isoclinismisoclinic class of #1132
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#89254

Splittings

FittingC42×C7×C8 ⋊ C2
SylowC7 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42D28
commutatorC4×C7C2×C4×C8
FrattiniC2×C42C22×D7
FittingC42×C7×C8C2
socleC23×C7C2×C22⋊C4
prime radicalC22×D28C2×C4
cosocleC2×C42×C7C23
hypercenterC42×C8D7
hypocenterC7C4×D4⋊C8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 60161);