Finite Group Databasebeta

C4×#90212 #13512033

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

Aliases

direct productC4×#90212

Splittings

FittingC4×C7×#117 ⋊ C2
SylowC7 ⋊ C4×#518

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC2×C7C23×C42
FrattiniC23C24×D7
FittingC4×C7×#117C2
socle, cosocleC23×C7C25
prime radicalC23×D28C22
hypercenterC4×#117D7
hypocenterC7C4×#518
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×#117

4186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 327805);