Finite Group Databasebeta

C2×#23762403 #34260486

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

Aliases

direct productC2×#23762403

Splittings

SylowC79 ⋊ C2×#1610

Subgroups

subgroupG/H
centerC23#14579130
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
Fitting, prime radicalC2×#537×C79C2
socleC23×C79#120
hypercenterC2×#537D79
hypocenterC79C2×#1610
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#537

1308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

1762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 141785);