Finite Group Databasebeta

← Prev (#28358324) Next (#28358326) →

C2×D3485 #28358325

order13940
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD6970
direct productC2×D3485
unambiguous semidirect product(C2×C5)⋊D697
unambiguous semidirect product(C2×C17)⋊D205
unambiguous semidirect product(C2×C41)⋊D85

Splittings

Fitting, socleC2×C5×C17×C41 ⋊ C2
derived, HallC5×C17×C41 ⋊ C22
HallC17×C41 ⋊ C2×D5
HallC5×C41 ⋊ C2×D17
HallC5×C17 ⋊ C2×D41
SylowC41 ⋊ C2×D85
SylowC17 ⋊ C2×D205
SylowC5 ⋊ C2×D697

Subgroups

subgroupG/H
center, hypercenterC2D3485
commutator, cosocle, hypocenterC5×C17×C41C22
FrattiniC1G
Fitting, socleC2×C5×C17×C41C2
LCSG ▷ C5×C17×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 6970

A minimal faithful permutation representation — 2 generators on 65 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);(4,7)(5,6)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

3488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13940
maximal normal subgroup ofD13940
maximal quotient ofD13940, Dic6970

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13940, 60);