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Cayley diagram

C2×C5⋊D25 #92546

order500
isoclinismisoclinic class of C5⋊D25
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5⋊D25
unambiguous semidirect product(C2×C5)⋊D25
unambiguous semidirect product(C2×C25)⋊D5

Splittings

FittingC2×C5×C25 ⋊ C2
derived, SylowC5×C25 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2C5⋊D25
commutator, cosocle, hypocenterC5×C25C22
FrattiniC5C2×C5⋊D5
FittingC2×C5×C25C2
socleC2×C52D5
LCSG ▷ C5×C25
UCSC1 ◁ C2

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 250

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2)(4,5)(6,7)(9,11)(10,14)(12,17)(13,20)(15,23)(16,22)(18,19)(21,27)(24,28)(25,29)(26,31)(30,32);(1,2)(3,4,6,7,5);(8,22,32,25,11,14,28,26,17,20,23,21,19,18,27,15,13,12,31,24,10,9,29,30,16)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11758652, #11758653, #11758656, …
maximal normal subgroup of#11758652, #11758653, #11758656, …
maximal quotient of#11758682, C4×C5⋊D25, C4⋊(C5⋊D25), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(500, 32);