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Cayley diagram

D5×D21 #88303

order420
isoclinismisoclinic class of D5×D21
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D21
unambiguous semidirect product(C3×D5)⋊D7
unambiguous semidirect product(C7×D5)⋊D3

Splittings

Fitting, socle, derived, HallC3×C5×C7 ⋊ C22
HallC5×C7 ⋊ C2×D3
HallC3×C7 ⋊ C2×D5
HallC3×C5 ⋊ C2×D7
SylowC7 ⋊ D3×D5
SylowC5 ⋊ C2×D21
SylowC3 ⋊ D5×D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7C22
LCSG ▷ C3×C5×C7
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 105

A minimal faithful permutation representation — 2 generators on 15 points:

(2,3)(4,5)(6,7)(9,10)(11,12,14,15,13);(1,2,4,6,7,5,3)(8,9,10)(12,13)(14,15)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×D21, D21⋊AGL(1,𝔽5), D3×D5×D7, …
maximal normal subgroup ofAGL(1,𝔽5)×D21, D21⋊AGL(1,𝔽5), D3×D5×D7, …
maximal quotient ofDic5×D21, D5×Dic21, #11719770, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(420, 28);