Finite Group Databasebeta

C23×#6435 #14260354

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#6435

Splittings

FittingC23×C42×C7 ⋊ C2
SylowC7 ⋊ C23×#117

Subgroups

subgroupG/H
centerC24×C4C2×D7
commutatorC2×C7C25×C4
FrattiniC22C25×D7
FittingC23×C42×C7C2
socleC25×C7C23
prime radicalC25×D7C22
cosocleC22×C7C26
hypercenterC23×C42D7
hypocenterC7C23×#117
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C24×C4 ◁ C23×C42

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1076126);