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C2×C4⋊(C3⋊(C5⋊D5)) #11925717

order1200
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23×C5

Aliases

direct productC2×C4⋊(C3⋊(C5⋊D5))

Splittings

FittingC2×C3×C4×C52 ⋊ C2
HallC3×C52 ⋊ C2×D4
SylowC52 ⋊ C2×D12
SylowC3 ⋊ C2×C4⋊(C5⋊D5)

Subgroups

subgroupG/H
centerC22C2×C3⋊(C5⋊D5)
commutator, cosocleC2×C3×C52C23
FrattiniC2C22×C3⋊(C5⋊D5)
FittingC2×C3×C4×C52C2
socleC22×C3×C52C22
hypercenterC2×C4C3⋊(C5⋊D5)
hypocenterC3×C52C2×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22 ◁ C2×C4

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×D12×C5⋊D5, C2×D4×C3⋊(C5⋊D5), C2×D3×C4⋊(C5⋊D5), …
maximal normal subgroup ofC2×D12×C5⋊D5, C2×D4×C3⋊(C5⋊D5), C2×D3×C4⋊(C5⋊D5), …
maximal quotient of#72229734, C2×C4⋊(C3⋊(C3⋊(C5⋊D5))), C2×#14268293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 927);