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C2×D4623 #32914980

order18492
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9246
direct productC2×D4623
unambiguous semidirect product(C2×C3)⋊D1541
unambiguous semidirect product(C2×C23)⋊D201
unambiguous semidirect product(C2×C67)⋊D69

Splittings

Fitting, socleC2×C3×C23×C67 ⋊ C2
derived, HallC3×C23×C67 ⋊ C22
HallC23×C67 ⋊ C2×D3
HallC3×C67 ⋊ C2×D23
HallC3×C23 ⋊ C2×D67
SylowC67 ⋊ C2×D69
SylowC23 ⋊ C2×D201
SylowC3 ⋊ C2×D1541

Subgroups

subgroupG/H
center, hypercenterC2D4623
commutator, cosocle, hypocenterC3×C23×C67C22
FrattiniC1G
Fitting, socleC2×C3×C23×C67C2
LCSG ▷ C3×C23×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 9246

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

Conjugacy classes & character table

4626 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18492, C2×D13869
maximal normal subgroup ofD18492
maximal quotient ofDic9246, D18492, C2×D13869

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18492, 28);