Finite Group Databasebeta

C4×#89766 #13275652

order1792
isoclinismisoclinic class of #89428
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#89766

Splittings

FittingC2×C4×C7×C4⋊C4 ⋊ C2
SylowC7 ⋊ C4×#396

Subgroups

subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×C4×C4⋊C4D7
hypocenterC7C4×#396
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1966 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, 91424);