Finite Group Databasebeta

← Prev (#40996005) Next (#40996007) →

C2×D6601 #40996006

order26404
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13202
direct productC2×D6601
unambiguous semidirect product(C2×C7)⋊D943
unambiguous semidirect product(C2×C23)⋊D287
unambiguous semidirect product(C2×C41)⋊D161

Splittings

Fitting, socleC2×C7×C23×C41 ⋊ C2
derived, HallC7×C23×C41 ⋊ C22
HallC23×C41 ⋊ C2×D7
HallC7×C41 ⋊ C2×D23
HallC7×C23 ⋊ C2×D41
SylowC41 ⋊ C2×D161
SylowC23 ⋊ C2×D287
SylowC7 ⋊ C2×D943

Subgroups

subgroupG/H
center, hypercenterC2D6601
commutator, cosocle, hypocenterC7×C23×C41C22
FrattiniC1G
Fitting, socleC2×C7×C23×C41C2
LCSG ▷ C7×C23×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 13202

A minimal faithful permutation representation — 2 generators on 73 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);(4,9)(5,8)(6,7)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(34,73)(35,72)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Conjugacy classes & character table

6604 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26404
maximal normal subgroup ofD26404
maximal quotient ofDic13202, D26404

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26404, 27);