Finite Group Databasebeta

← Prev (#72292688) Next (#72292690) →

C2×D14553 #72292689

order58212
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD29106
direct productC2×D14553

Splittings

FittingC2×C11×C27×C49 ⋊ C2
derived, HallC11×C27×C49 ⋊ C22
HallC27×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×D27
HallC11×C27 ⋊ C2×D49
SylowC49 ⋊ C2×D297
SylowC27 ⋊ C2×D539
SylowC11 ⋊ C2×D1323

Subgroups

subgroupG/H
center, hypercenterC2D14553
commutator, cosocle, hypocenterC11×C27×C49C22
FrattiniC7×C9C2×D231
FittingC2×C11×C27×C49C2
socleC2×C3×C7×C11D63
LCSG ▷ C11×C27×C49
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 89
transitive degreeμt(G) = 29106

A minimal faithful permutation representation — 2 generators on 89 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)(79,80,81,82,83,84,85,86,87,88,89);(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,78)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)(80,89)(81,88)(82,87)(83,86)(84,85)

Conjugacy classes & character table

14556 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((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)(79,80,81,82,83,84,85,86,87,88,89), (4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,78)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)(80,89)(81,88)(82,87)(83,86)(84,85));