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C5×#3773 #10623999

order720
isoclinismisoclinic class of GO+(4,𝔽2)
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#3773

Splittings

HallC32×C5 ⋊ C4⋊C4
SylowC32 ⋊ C5×C4⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5GO+(4,𝔽2)
commutatorC3⋊D3C2×C4×C5
FrattiniC2C5×GO+(4,𝔽2)
Fitting, socleC2×C32×C5D4
prime radicalC2×C5×C3⋊D3C22
cosocleC2×C3⋊D3C22×C5
hypocenterC32C5×C4⋊C4
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×PSU(3,𝔽2)⋊C4, C5×AGL(1,𝔽9)⋊C4, #13088394, …
maximal normal subgroup ofC5×PSU(3,𝔽2)⋊C4, C5×AGL(1,𝔽9)⋊C4, #13088394, …
maximal quotient ofC5×#63732, C5×#63733, C5×#63737, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 468);