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C3×C31⋊C8 #10625213

order744
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×C31⋊C8

Splittings

derived, SylowC31 ⋊ C3×C8
HallC3×C31 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC3×C4D31
commutator, hypocenterC31C3×C8
FrattiniC4C3×D31
FittingC3×C4×C31C2
socle, prime radicalC2×C3×C31C4
cosocleC4×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C3×C4

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 744

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36,37,39,38,40,41,42);(4,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6)

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C31⋊C8, D93⋊C8, #13093431, …
maximal normal subgroup ofD3×C31⋊C8, D93⋊C8, #13093431, …
maximal quotient ofC3×C31⋊C16, C2×C3×C31⋊C8

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(744, 4);