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Cayley diagram

D4×D29 #90806

order464
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD4×D29

Splittings

FittingD4×C29 ⋊ C2
SylowC29 ⋊ C2×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×D29
commutator, socle, cosocleC2×C29C23
FittingD4×C29C2
hypercenterD4D29
hypocenterC29C2×D4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ D4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 116

A minimal faithful permutation representation — 3 generators on 33 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);(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)(31,33);(30,31)(32,33)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745223, D8×D29, #11745273, …
maximal normal subgroup of#11745223, D8×D29, #11745273, …
maximal quotient of#11745240, C22⋊C4×D29, #11745243, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 39);