Finite Group Databasebeta

← Prev (#35202153) Next (#35202155) →

C22×H(5,𝔽2)×D79 #35202154

order20224
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC22×H(5,𝔽2)×D79

Splittings

FittingC22×H(5,𝔽2)×C79 ⋊ C2
SylowC79 ⋊ C23×H(5,𝔽2)

Subgroups

subgroupG/H
centerC23C24×D79
commutator, cosocleC2×C79C27
FrattiniC2C26×D79
FittingC22×H(5,𝔽2)×C79C2
socleC23×C79C25
hypercenterC22×H(5,𝔽2)D79
hypocenterC79C23×H(5,𝔽2)
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

65726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2528

Conjugacy classes & character table

2788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1083453);