Finite Group Databasebeta

C2×#23778003 #35195654

order20224
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#23778003

Splittings

SylowC79 ⋊ C2×#3563

Subgroups

subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#529×C79C2
socleC23×C79C25
prime radicalC2×#121×C79C22
hypercenterC2×#529D79
hypocenterC79C2×#3563
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#529

6458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

2260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1076953);