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C42×C31⋊C3 #13093452

order1488
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C4

Aliases

direct productC42×C31⋊C3

Splittings

Fitting, HallC42×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C42

Subgroups

subgroupG/H
center, hypercenterC42C31⋊C3
commutator, hypocenterC31C3×C42
FrattiniC22C22×C31⋊C3
FittingC42×C31C3
socle, cosocleC22×C31C22×C3
prime radicalC22×C31⋊C3C22
LCSG ▷ C31
UCSC1 ◁ C42

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 496

A minimal faithful permutation representation — 2 generators on 39 points:

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

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#127×C31⋊C3, C42×D31⋊C3, #72277808, …
maximal normal subgroup of#127×C31⋊C3, C42×D31⋊C3, #72277808, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1488, 48);