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C23×#3992 #13044377

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210

Aliases

direct productC23×#3992

Splittings

FittingC23×C5×C8 ⋊ C4
SylowC5 ⋊ C23×#97

Subgroups

subgroupG/H
centerC23×C4C2×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FrattiniC4C24×AGL(1,𝔽5)
FittingC23×C5×C8C4
socleC24×C5C42
prime radicalC24×D5C2×C4
cosocleC4×D5C25
hypercenterC23×C8AGL(1,𝔽5)
hypocenterC5C23×#97
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C23×C8

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×AGL(1,𝔽5)×#97, C23×#11716763
maximal normal subgroup ofC22×AGL(1,𝔽5)×#97
maximal quotient ofC23×#11716763

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114645);