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AGL(1,𝔽5)×#62817 #72243140

order5120
automorphism?
homologyAbelianization (H1) = C26×C4 · Schur multiplier (H2) = C219

Aliases

direct productAGL(1,𝔽5)×#62817

Splittings

FittingC5×#62817 ⋊ C4
SylowC5 ⋊ C4×#62817

Subgroups

subgroupG/H
center, FrattiniC22C26×AGL(1,𝔽5)
commutator, socleC22×C5C26×C4
FittingC5×#62817C4
prime radicalD5×#62817C2
cosocleC22×D5C27
hypercenter#62817AGL(1,𝔽5)
hypocenterC5C4×#62817
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #62817

179586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽5)×#11710731, AGL(1,𝔽5)×#511790, AGL(1,𝔽5)×#347042, …
maximal normal subgroup ofAGL(1,𝔽5)×#11710731, AGL(1,𝔽5)×#511790, AGL(1,𝔽5)×#347042, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.