Finite Group Databasebeta

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Cayley diagram

C22×Dic29 #90810

order464
isoclinismisoclinic class of D29
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×Dic29

Splittings

derived, SylowC29 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC23D29
commutator, hypocenterC29C22×C4
FrattiniC2C22×D29
Fitting, socle, prime radicalC23×C29C2
cosocleC2×C29C23
LCSG ▷ C29
UCSC1 ◁ C23

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 464

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2)(3,4)(5,6,7,8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37);(3,4)(9,10,12,14,16,18,20,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23,21,19,17,15,13,11);(1,2)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745179, C22⋊#6599, #11745239, …
maximal normal subgroup of#11745179, C22⋊#6599, #11745239, …
maximal quotient ofC22×#6597, C2×#90777, C2×C4×Dic29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 43);