Finite Group Databasebeta

C2×#23762855 #34270666

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

Aliases

direct productC2×#23762855

Splittings

SylowC79 ⋊ C2×#1684

Subgroups

subgroupG/H
centerC23#14579132
commutator, cosocleC42×C79C24
FrattiniC42C23×D79
FittingC2×#487×C79C2
socle, prime radicalC23×C79#121
hypercenterC2×#487D79
hypocenterC79C2×#1684
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20224

Conjugacy classes & character table

1774 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 151965);