Finite Group Databasebeta

← Prev (#11927607) Next (#11927609) →

C2×C3×C41⋊C5 #11927608

order1230
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C41⋊C5
unambiguous semidirect product(C2×C41)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C41)⋊C5

Splittings

Fitting, socle, HallC2×C3×C41 ⋊ C5
derived, SylowC41 ⋊ C2×C3×C5
HallC3×C41 ⋊ C2×C5
HallC2×C41 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C41⋊C5
commutator, cosocle, hypocenterC41C2×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C41C5
LCSG ▷ C41
UCSC1 ◁ C2×C3

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 246

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2)(3,4,5)(7,8,10,14,22)(9,12,18,29,40)(11,16,25,17,27)(13,20,28,39,26)(15,24,35,23,34)(19,30,41,45,38)(21,33,32,43,46)(31,42,36,44,37);(6,7,9,13,21,30,34,39,45,41,8,11,17,28,35,42,14,23,10,15,12,19,31,43,44,46,24,36,16,26,20,32,29,40,25,37,18,22,27,38,33)

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×Dic41⋊C5, Dic3×C41⋊C5, C3⋊(Dic41⋊C5), …
maximal normal subgroup ofC3×Dic41⋊C5, Dic3×C41⋊C5, C3⋊(Dic41⋊C5), …
maximal quotient ofC3×C4×C41⋊C5, C22×C3×C41⋊C5, C2×C9×C41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1230, 4);