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Cayley diagram

D3×D25 #64464

order300
isoclinismisoclinic class of D3×D25
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D25
unambiguous semidirect product(D3×C25)⋊C2
unambiguous semidirect product(C3×D25)⋊C2
unambiguous semidirect productD75⋊C2

Splittings

Fitting, derived, HallC3×C25 ⋊ C22
SylowC25 ⋊ C2×D3
SylowC3 ⋊ C2×D25

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C25C22
FrattiniC5D3×D5
socleC3×C5C2×D5
LCSG ▷ C3×C25
UCSC1

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 75

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#1035, C2×D3×D25, D9×D25, …
maximal normal subgroup ofD3×#1035, C2×D3×D25, C3×D3×D25, …
maximal quotient of#10597026, Dic3×D25, #10597028, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 7);