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C13×#1181 #13094085

order1508
isoclinismisoclinic class of #1181
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#1181

Splittings

Fitting, socle, HallC13×C29 ⋊ C4
derived, SylowC29 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC13#1181
commutator, hypocenterC29C4×C13
FrattiniC1G
Fitting, socleC13×C29C4
prime radicalC13×D29C2
cosocleD29C2×C13
LCSG ▷ C29
UCSC1 ◁ C13

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 377

A minimal faithful permutation representation — 2 generators on 42 points:

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

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13⋊C3×#1181, C3×C13×#1181, C13×C3⋊#1181, …
maximal normal subgroup ofC13⋊C3×#1181, C3×C13×#1181, C11×C13×#1181, …
maximal quotient ofC3×C13×#1181, C13×C3⋊#1181, C13×#11760329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1508, 5);