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C2×D4845 #34084402

order19380
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9690
direct productC2×D4845
unambiguous semidirect product(C2×C3)⋊D1615
unambiguous semidirect product(C2×C5)⋊D969
unambiguous semidirect product(C2×C17)⋊D285
unambiguous semidirect product(C2×C19)⋊D255

Splittings

Fitting, socleC2×C3×C5×C17×C19 ⋊ C2
derived, HallC3×C5×C17×C19 ⋊ C22
HallC5×C17×C19 ⋊ C2×D3
HallC3×C17×C19 ⋊ C2×D5
HallC17×C19 ⋊ C2×D15
HallC3×C5×C19 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D19
HallC5×C19 ⋊ C2×D51
HallC5×C17 ⋊ C2×D57
HallC3×C19 ⋊ C2×D85
HallC3×C17 ⋊ C2×D95
SylowC19 ⋊ C2×D255
SylowC17 ⋊ C2×D285
HallC3×C5 ⋊ C2×D323
SylowC5 ⋊ C2×D969
SylowC3 ⋊ C2×D1615

Subgroups

subgroupG/H
center, hypercenterC2D4845
commutator, cosocle, hypocenterC3×C5×C17×C19C22
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C19C2
LCSG ▷ C3×C5×C17×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 9690

A minimal faithful permutation representation — 2 generators on 46 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);(4,5)(7,10)(8,9)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Conjugacy classes & character table

4848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19380, C2×D14535
maximal normal subgroup ofD19380
maximal quotient ofDic9690, D19380, C2×D14535

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 114);