Finite Group Databasebeta

← Prev (#40997976) Next (#40997978) →

C2×D6643 #40997977

order26572
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13286
direct productC2×D6643
unambiguous semidirect product(C2×C7)⋊D949
unambiguous semidirect product(C2×C13)⋊D511
unambiguous semidirect product(C2×C73)⋊D91

Splittings

Fitting, socleC2×C7×C13×C73 ⋊ C2
derived, HallC7×C13×C73 ⋊ C22
HallC13×C73 ⋊ C2×D7
HallC7×C73 ⋊ C2×D13
HallC7×C13 ⋊ C2×D73
SylowC73 ⋊ C2×D91
SylowC13 ⋊ C2×D511
SylowC7 ⋊ C2×D949

Subgroups

subgroupG/H
center, hypercenterC2D6643
commutator, cosocle, hypocenterC7×C13×C73C22
FrattiniC1G
Fitting, socleC2×C7×C13×C73C2
LCSG ▷ C7×C13×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 13286

A minimal faithful permutation representation — 2 generators on 95 points:

(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(4,9)(5,8)(6,7)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(24,95)(25,94)(26,93)(27,92)(28,91)(29,90)(30,89)(31,88)(32,87)(33,86)(34,85)(35,84)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

6646 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26572
maximal normal subgroup ofD26572
maximal quotient ofDic13286, D26572

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26572, 35);