Finite Group Databasebeta

← Prev (#46799644) Next (#46799646) →

C2×D8463 #46799645

order33852
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16926
direct productC2×D8463
unambiguous semidirect product(C2×C3)⋊D2821
unambiguous semidirect product(C2×C7)⋊D1209
unambiguous semidirect product(C2×C13)⋊D651
unambiguous semidirect product(C2×C31)⋊D273

Splittings

Fitting, socleC2×C3×C7×C13×C31 ⋊ C2
derived, HallC3×C7×C13×C31 ⋊ C22
HallC7×C13×C31 ⋊ C2×D3
HallC3×C13×C31 ⋊ C2×D7
HallC3×C7×C31 ⋊ C2×D13
HallC13×C31 ⋊ C2×D21
HallC3×C7×C13 ⋊ C2×D31
HallC7×C31 ⋊ C2×D39
HallC3×C31 ⋊ C2×D91
HallC7×C13 ⋊ C2×D93
HallC3×C13 ⋊ C2×D217
SylowC31 ⋊ C2×D273
HallC3×C7 ⋊ C2×D403
SylowC13 ⋊ C2×D651
SylowC7 ⋊ C2×D1209
SylowC3 ⋊ C2×D2821

Subgroups

subgroupG/H
center, hypercenterC2D8463
commutator, cosocle, hypocenterC3×C7×C13×C31C22
FrattiniC1G
Fitting, socleC2×C3×C7×C13×C31C2
LCSG ▷ C3×C7×C13×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 16926

A minimal faithful permutation representation — 2 generators on 56 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);(4,5)(7,12)(8,11)(9,10)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(27,56)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

8466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 440);