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C2×#10624098 #13089161

order1440
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct productC2×#10624098
unambiguous semidirect productD5⋊#3757

Splittings

FittingC23×C32×C5 ⋊ C4
HallC32×C5 ⋊ C2×C22⋊C4
SylowC32 ⋊ C2×C22⋊AGL(1,𝔽5)
SylowC5 ⋊ C2×#3757

Subgroups

subgroupG/H
centerC22C2×C3⋊ΓL(1,𝔽16)
commutatorC2×C32×C5C22×C4
FrattiniC2C22×C3⋊ΓL(1,𝔽16)
FittingC23×C32×C5C4
socleC22×C32×C5C2×C4
prime radicalC23×C32×D5C2
cosocleC2×C32×D5C23
hypercenterC23C3⋊ΓL(1,𝔽16)
hypocenterC32×C5C2×C22⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

792 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D4×C3⋊ΓL(1,𝔽16), C2×AGL(1,𝔽5)×#638, C2×C3⋊D3×C22⋊AGL(1,𝔽5), …
maximal normal subgroup ofC2×D4×C3⋊ΓL(1,𝔽16), C2×AGL(1,𝔽5)×#638, C2×C3⋊D3×C22⋊AGL(1,𝔽5), …
maximal quotient of#72229915, #72229980, C2×#72229600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5478);