Finite Group Databasebeta

C2×#23767379 #34456259

order20224
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#23767379

Splittings

SylowC79 ⋊ C2×#2462

Subgroups

subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#387×C79C2
socle, prime radicalC24×C79C24
hypercenterC2×#387D79
hypocenterC79C2×#2462
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#387

2486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20224

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, 337558);