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C2×D7847 #44536014

order31388
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15694
direct productC2×D7847
unambiguous semidirect product(C2×C7)⋊D1121
unambiguous semidirect product(C2×C19)⋊D413
unambiguous semidirect product(C2×C59)⋊D133

Splittings

Fitting, socleC2×C7×C19×C59 ⋊ C2
derived, HallC7×C19×C59 ⋊ C22
HallC19×C59 ⋊ C2×D7
HallC7×C59 ⋊ C2×D19
HallC7×C19 ⋊ C2×D59
SylowC59 ⋊ C2×D133
SylowC19 ⋊ C2×D413
SylowC7 ⋊ C2×D1121

Subgroups

subgroupG/H
center, hypercenterC2D7847
commutator, cosocle, hypocenterC7×C19×C59C22
FrattiniC1G
Fitting, socleC2×C7×C19×C59C2
LCSG ▷ C7×C19×C59
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 87
transitive degreeμt(G) = 15694

A minimal faithful permutation representation — 2 generators on 87 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);(4,9)(5,8)(6,7)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(30,87)(31,86)(32,85)(33,84)(34,83)(35,82)(36,81)(37,80)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)

Conjugacy classes & character table

7850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31388
maximal normal subgroup ofD31388
maximal quotient ofDic15694, D31388

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31388, 23);