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C22⋊C4×C31⋊C3 #13093453

order1488
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC22⋊C4×C31⋊C3
unambiguous semidirect product(C22⋊C4×C31)⋊C3

Splittings

Fitting, HallC22⋊C4×C31 ⋊ C3
SylowC31 ⋊ C3×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×C31⋊C3
commutatorC2×C31C2×C3×C4
FittingC22⋊C4×C31C3
socle, cosocleC22×C31C22×C3
prime radicalC23×C31⋊C3C2
hypercenterC22⋊C4C31⋊C3
hypocenterC31C3×C22⋊C4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22⋊C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 248

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

(1,2,4,6)(3,5,7,8)(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);(2,5)(6,8)(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

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1488, 49);