Finite Group Databasebeta

C4×#89732 #13275582

order1792
isoclinismisoclinic class of #89428
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#89732

Splittings

FittingC2×C4×C7×C22⋊C4 ⋊ C2
SylowC7 ⋊ C4×#392

Subgroups

subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C4×#392
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

3502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 91354);