Finite Group Databasebeta

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Cayley diagram

C2×#6597 #90776

order464
isoclinismisoclinic class of D29
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

direct productC2×#6597

Splittings

derived, SylowC29 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4D29
commutator, hypocenterC29C2×C8
FrattiniC4C2×D29
FittingC2×C4×C29C2
socle, prime radicalC22×C29C4
cosocleC4×C29C22
LCSG ▷ C29
UCSC1 ◁ C2×C4

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 464

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2)(3,4,5,7,6,8,9,10)(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)(38,39);(1,2)(11,12,14,16,18,20,22,24,26,28,30,32,34,36,38,39,37,35,33,31,29,27,25,23,21,19,17,15,13)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#6597, #11745151, C4⋊#6597, …
maximal normal subgroup ofC4×#6597, #11745151, C4⋊#6597, …
maximal quotient ofC4×#6597, C4⋊#6597, C2×#90768, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 9);