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C2×D7735 #44525973

order30940
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15470
direct productC2×D7735
unambiguous semidirect product(C2×C5)⋊D1547
unambiguous semidirect product(C2×C7)⋊D1105
unambiguous semidirect product(C2×C13)⋊D595
unambiguous semidirect product(C2×C17)⋊D455

Splittings

Fitting, socleC2×C5×C7×C13×C17 ⋊ C2
derived, HallC5×C7×C13×C17 ⋊ C22
HallC7×C13×C17 ⋊ C2×D5
HallC5×C13×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×D65
HallC7×C13 ⋊ C2×D85
HallC5×C17 ⋊ C2×D91
HallC5×C13 ⋊ C2×D119
HallC5×C7 ⋊ C2×D221
SylowC17 ⋊ C2×D455
SylowC13 ⋊ C2×D595
SylowC7 ⋊ C2×D1105
SylowC5 ⋊ C2×D1547

Subgroups

subgroupG/H
center, hypercenterC2D7735
commutator, cosocle, hypocenterC5×C7×C13×C17C22
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C17C2
LCSG ▷ C5×C7×C13×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 15470

A minimal faithful permutation representation — 2 generators on 44 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);(4,7)(5,6)(9,14)(10,13)(11,12)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

7738 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30940
maximal normal subgroup ofD30940
maximal quotient ofDic15470, D30940

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 123);