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C3×D4697 #43245308

order28182
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4697
unambiguous semidirect productC11⋊(C3×D427)

Splittings

Fitting, socle, HallC3×C7×C11×C61 ⋊ C2
derived, HallC7×C11×C61 ⋊ C2×C3
HallC3×C11×C61 ⋊ D7
HallC3×C7×C61 ⋊ D11
HallC11×C61 ⋊ C3×D7
HallC7×C61 ⋊ C3×D11
HallC3×C7×C11 ⋊ D61
HallC3×C61 ⋊ D77
HallC7×C11 ⋊ C3×D61
SylowC61 ⋊ C3×D77
HallC3×C11 ⋊ D427
HallC3×C7 ⋊ D671
SylowC11 ⋊ C3×D427
SylowC7 ⋊ C3×D671

Subgroups

subgroupG/H
center, hypercenterC3D4697
commutator, cosocle, hypocenterC7×C11×C61C2×C3
FrattiniC1G
Fitting, socleC3×C7×C11×C61C2
LCSG ▷ C7×C11×C61
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 82
transitive degreeμt(G) = 14091

A minimal faithful permutation representation — 2 generators on 82 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82);(5,10)(6,9)(7,8)(12,21)(13,20)(14,19)(15,18)(16,17)(23,82)(24,81)(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

7050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28182, 12);