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C3×#17985236 #27214272

order13530
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#17985236

Splittings

Fitting, socle, HallC3×C11×C41 ⋊ C2×C5
derived, HallC11×C41 ⋊ C2×C3×C5
HallC3×#14555917 ⋊ C2
HallC3×C11×D41 ⋊ C5
Hall#14555917 ⋊ C2×C3
HallC11×D41 ⋊ C3×C5
HallC3×D41 ⋊ C11⋊C5
HallC3×C41 ⋊ C2×C11⋊C5
HallD41 ⋊ C3×C11⋊C5
SylowC41 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ D41⋊C5
SylowC11 ⋊ C3×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#17985236
commutator, cosocle, hypocenterC11×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C41C2×C5
LCSG ▷ C11×C41
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 1353

A minimal faithful permutation representation — 2 generators on 55 points:

(2,6,7,22,25,3,4,12,14,24)(5,19,20,31,32,9,10,33,18,41)(8,28,29,30,23,16,17,39,36,13)(11,27,35,26,40,15,21,38,37,34)(43,44,46,49,48)(45,47,51,52,50)(53,54,55);(1,2,5,11,12,19,29,40,33,41,14,26,38,21,17,30,25,23,4,8,18,31,16,6,13,24,36,28,27,35,37,22,32,20,34,39,10,7,15,9,3)(42,43,45,48,44,46,50,52,47,49,51)

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#22583167, C3×#17985236⋊C2, C3×#22583177, …
maximal normal subgroup ofC3×#22583167, C3×#17985236⋊C2, C3×#22583177, …
maximal quotient ofC3×#22583147, C2×C3×#17985236

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13530, 26);