Finite Group Databasebeta

C2×#23764926 #34318032

order20224
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#23764926

Splittings

SylowC79 ⋊ C2×#2093

Subgroups

subgroupG/H
centerC24D4×D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC22×#102×C79C2
socleC24×C79C2×D4
prime radicalC23×D4×C79C22
hypercenterC22×#102D79
hypocenterC79C2×#2093
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

2248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 199331);