Finite Group Databasebeta

← Prev (#41029901) Next (#41029903) →

C2×D6789 #41029902

order27156
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13578
direct productC2×D6789
unambiguous semidirect product(C2×C3)⋊D2263
unambiguous semidirect product(C2×C31)⋊D219
unambiguous semidirect product(C2×C73)⋊D93

Splittings

Fitting, socleC2×C3×C31×C73 ⋊ C2
derived, HallC3×C31×C73 ⋊ C22
HallC31×C73 ⋊ C2×D3
HallC3×C73 ⋊ C2×D31
HallC3×C31 ⋊ C2×D73
SylowC73 ⋊ C2×D93
SylowC31 ⋊ C2×D219
SylowC3 ⋊ C2×D2263

Subgroups

subgroupG/H
center, hypercenterC2D6789
commutator, cosocle, hypocenterC3×C31×C73C22
FrattiniC1G
Fitting, socleC2×C3×C31×C73C2
LCSG ▷ C3×C31×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 109
transitive degreeμt(G) = 13578

A minimal faithful permutation representation — 2 generators on 109 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(4,5)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(38,109)(39,108)(40,107)(41,106)(42,105)(43,104)(44,103)(45,102)(46,101)(47,100)(48,99)(49,98)(50,97)(51,96)(52,95)(53,94)(54,93)(55,92)(56,91)(57,90)(58,89)(59,88)(60,87)(61,86)(62,85)(63,84)(64,83)(65,82)(66,81)(67,80)(68,79)(69,78)(70,77)(71,76)(72,75)(73,74)

Conjugacy classes & character table

6792 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD27156
maximal normal subgroup ofD27156
maximal quotient ofDic13578, D27156

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27156, 76);