Finite Group Databasebeta

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C2×D8211 #45659339

order32844
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16422
direct productC2×D8211
unambiguous semidirect product(C2×C3)⋊D2737
unambiguous semidirect product(C2×C7)⋊D1173
unambiguous semidirect product(C2×C17)⋊D483
unambiguous semidirect product(C2×C23)⋊D357

Splittings

Fitting, socleC2×C3×C7×C17×C23 ⋊ C2
derived, HallC3×C7×C17×C23 ⋊ C22
HallC7×C17×C23 ⋊ C2×D3
HallC3×C17×C23 ⋊ C2×D7
HallC3×C7×C23 ⋊ C2×D17
HallC17×C23 ⋊ C2×D21
HallC3×C7×C17 ⋊ C2×D23
HallC7×C23 ⋊ C2×D51
HallC7×C17 ⋊ C2×D69
HallC3×C23 ⋊ C2×D119
HallC3×C17 ⋊ C2×D161
SylowC23 ⋊ C2×D357
HallC3×C7 ⋊ C2×D391
SylowC17 ⋊ C2×D483
SylowC7 ⋊ C2×D1173
SylowC3 ⋊ C2×D2737

Subgroups

subgroupG/H
center, hypercenterC2D8211
commutator, cosocle, hypocenterC3×C7×C17×C23C22
FrattiniC1G
Fitting, socleC2×C3×C7×C17×C23C2
LCSG ▷ C3×C7×C17×C23
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 16422

A minimal faithful permutation representation — 2 generators on 52 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);(4,5)(7,12)(8,11)(9,10)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(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

8214 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 104);