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C2×C8×C31⋊C3 #13093455

order1488
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2

Aliases

direct productC2×C8×C31⋊C3
unambiguous semidirect product(C2×C8×C31)⋊C3

Splittings

Fitting, HallC2×C8×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C3×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8C31⋊C3
commutator, hypocenterC31C2×C3×C8
FrattiniC4C22×C31⋊C3
FittingC2×C8×C31C3
socleC22×C31C3×C4
prime radicalC22×C31⋊C3C4
cosocleC4×C31C22×C3
LCSG ▷ C31
UCSC1 ◁ C2×C8

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 496

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2)(12,13,15)(14,17,22)(16,20,19)(18,24,31)(21,27,29)(23,25,26)(28,34,38)(30,35,36)(32,39,33)(37,40,41);(3,4,5,6,7,8,9,10)(11,12,14,18,25,15,19,26,33,39,22,29,36,24,32,31,38,41,34,17,23,30,37,40,27,13,16,21,28,35,20)

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1488, 51);