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C42×C13⋊C3 #10597614

order624
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C4

Aliases

direct productC42×C13⋊C3

Splittings

Fitting, HallC42×C13 ⋊ C3
derived, SylowC13 ⋊ C3×C42

Subgroups

subgroupG/H
center, hypercenterC42C13⋊C3
commutator, hypocenterC13C3×C42
FrattiniC22C22×C13⋊C3
FittingC42×C13C3
socle, cosocleC22×C13C22×C3
prime radicalC22×C13⋊C3C22
LCSG ▷ C13
UCSC1 ◁ C42

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 208

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#1055⋊C3, #88043⋊C3, C4⋊(#1055⋊C3), …
maximal normal subgroup ofC4×#1055⋊C3, #88043⋊C3, C4⋊(#1055⋊C3), …
maximal quotient of#95×C13⋊C3, C4×C8×C13⋊C3, #97×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(624, 51);