Finite Group Databasebeta

← Prev (#16838444) Next (#16838446) →

C13×#64424 #16838445

order3822
isoclinismisoclinic class of #64424
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#64424

Splittings

Fitting, socle, HallC72×C13 ⋊ C2×C3
derived, SylowC72 ⋊ C2×C3×C13
HallC13×#3861 ⋊ C2
HallC13×C7⋊D7 ⋊ C3
Hall#3861 ⋊ C2×C13
HallC7⋊D7 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC13#64424
commutator, cosocle, hypocenterC72C2×C3×C13
FrattiniC1G
Fitting, socleC72×C13C2×C3
LCSG ▷ C72
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 637

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19,18,16,17,20)(22,26,25,23,24,27);(21,22,25,26,24,27,23);(14,15,18,19,17,20,16)

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13⋊C3×#64424, C13×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #64424⋊(C13⋊C3), …
maximal normal subgroup ofC13⋊C3×#64424, C13×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #64424⋊(C13⋊C3), …
maximal quotient ofC13×#11725077, C3×C13×#64424, C13×C3⋊#64424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3822, 38);