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C13×#64422 #16838461

order3822
isoclinismisoclinic class of #64422
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#64422

Splittings

Fitting, socle, HallC72×C13 ⋊ C2×C3
derived, SylowC72 ⋊ C2×C3×C13
HallC13×#3862 ⋊ C2
HallC7×C13×D7 ⋊ C3
Hall#3862 ⋊ C2×C13
HallC7×D7 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC13#64422
commutator, cosocle, hypocenterC72C2×C3×C13
FrattiniC1G
Fitting, socleC72×C13C2×C3
LCSG ▷ C72
UCSC1 ◁ C13

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 546

A minimal faithful permutation representation — 2 generators on 27 points:

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

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×ΓL(1,𝔽8)×AGL(1,𝔽7), #26039539, #26039540, …
maximal normal subgroup ofC13×ΓL(1,𝔽8)×AGL(1,𝔽7), #26039539, #26039540, …
maximal quotient ofC13×#11725075, C3×C13×#64422, C13×C3⋊#64422, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3822, 54);