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C32×C22⋊(C5⋊D5) #14268327

order1800
isoclinismisoclinic class of #6045
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC32×C22⋊(C5⋊D5)

Splittings

FittingC22×C32×C52 ⋊ C2
HallC32×C52 ⋊ D4
SylowC52 ⋊ C32×D4

Subgroups

subgroupG/H
centerC2×C32C2×C5⋊D5
commutator, cosocleC2×C52C22×C32
FrattiniC2C2×C32×C5⋊D5
FittingC22×C32×C52C2
socleC2×C32×C52C22
hypercenterC22×C32C5⋊D5
hypocenterC52C32×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C32 ◁ C22×C32

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 900

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2,3)(8,10)(16,17,19,20,18);(4,5,6)(7,8)(9,10)(12,13)(14,15)(17,18)(19,20);(11,12,14,15,13)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC32×D4×C5⋊D5, C3⋊D3×C22⋊(C5⋊D5), #72230581, …
maximal normal subgroup ofC32×D4×C5⋊D5, C3⋊D3×C22⋊(C5⋊D5), #72230581, …
maximal quotient ofC2×C32×C22⋊(C5⋊D5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 521);