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Cayley diagram

D3×D29 #66828

order348
isoclinismisoclinic class of D3×D29
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D29
unambiguous semidirect product(D3×C29)⋊C2
unambiguous semidirect product(C3×D29)⋊C2
unambiguous semidirect productD87⋊C2

Splittings

Fitting, socle, derived, HallC3×C29 ⋊ C22
SylowC29 ⋊ C2×D3
SylowC3 ⋊ C2×D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C29C22
LCSG ▷ C3×C29
UCSC1

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 87

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#1181, C2×D3×D29, D9×D29, …
maximal normal subgroup ofD3×#1181, C2×D3×D29, C3×D3×D29, …
maximal quotient ofDic3×D29, D3×Dic29, #10621942, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(348, 7);