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C2×AGL(1,𝔽5)×#106 #13033570

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×AGL(1,𝔽5)×#106

Splittings

FittingC2×C5×#106 ⋊ C4
SylowC5 ⋊ C2×C4×#106

Subgroups

subgroupG/H
centerC23D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#106C4
socleC23×C5C4×D4
prime radicalC23×D5C2×D4
cosocleC2×C4×D5C24
hypercenterC2×#106AGL(1,𝔽5)
hypocenterC5C2×C4×#106
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

1358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#442, C2×AGL(1,𝔽5)×#365, C2×AGL(1,𝔽5)×#360, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#442, C2×AGL(1,𝔽5)×#365, C2×AGL(1,𝔽5)×#360, …
maximal quotient ofC2×AGL(1,𝔽5)×#365, C2×#106×#1043, #106×D5⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103838);