Finite Group Databasebeta

← Prev (#14274251) Next (#14274253) →

C13×C49⋊C3 #14274252

order1911
isoclinismisoclinic class of C49⋊C3
automorphism?
homologyAbelianization (H1) = C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C49⋊C3
unambiguous semidirect productC49⋊(C3×C13)

Splittings

Fitting, HallC13×C49 ⋊ C3
derived, SylowC49 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC13C49⋊C3
commutator, cosocle, hypocenterC49C3×C13
FrattiniC7C13×ΓL(1,𝔽8)
FittingC13×C49C3
socleC7×C13ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C13

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 637

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17,21)(16,20,29)(18,24,36)(19,27,42)(22,33,31)(23,34,45)(25,38,56)(26,32,28)(30,47,46)(35,53,58)(37,55,48)(39,44,57)(40,50,51)(41,52,54)(43,59,49)(60,61,62);(14,44,27,55,52,37,60,16,45,18,62,42,31,38,20,36,26,22,39,49,33,30,54,41,35,24,51,50,29,15,57,43,21,61,53,46,19,17,25,32,58,48,47,28,23,40,34,56,59)

Conjugacy classes & character table

247 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×C49⋊C3, C13×D49⋊C3, (C49⋊C3)⋊D13, …
maximal normal subgroup ofD13×C49⋊C3, C13×D49⋊C3, (C49⋊C3)⋊D13, …
maximal quotient ofC2×C13×C49⋊C3, C11×C13×C49⋊C3, C49⋊C3×C169, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1911, 1);