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C2×D4697 #34037706

order18788
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9394
direct productC2×D4697
unambiguous semidirect product(C2×C7)⋊D671
unambiguous semidirect product(C2×C11)⋊D427
unambiguous semidirect product(C2×C61)⋊D77

Splittings

Fitting, socleC2×C7×C11×C61 ⋊ C2
derived, HallC7×C11×C61 ⋊ C22
HallC11×C61 ⋊ C2×D7
HallC7×C61 ⋊ C2×D11
HallC7×C11 ⋊ C2×D61
SylowC61 ⋊ C2×D77
SylowC11 ⋊ C2×D427
SylowC7 ⋊ C2×D671

Subgroups

subgroupG/H
center, hypercenterC2D4697
commutator, cosocle, hypocenterC7×C11×C61C22
FrattiniC1G
Fitting, socleC2×C7×C11×C61C2
LCSG ▷ C7×C11×C61
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 9394

A minimal faithful permutation representation — 2 generators on 81 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);(4,9)(5,8)(6,7)(11,20)(12,19)(13,18)(14,17)(15,16)(22,81)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18788, C2×D14091
maximal normal subgroup ofD18788
maximal quotient ofDic9394, D18788, C2×D14091

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18788, 21);