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C2×D7347 #44440536

order29388
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD14694
direct productC2×D7347
unambiguous semidirect product(C2×C3)⋊D2449
unambiguous semidirect product(C2×C31)⋊D237
unambiguous semidirect product(C2×C79)⋊D93

Splittings

Fitting, socleC2×C3×C31×C79 ⋊ C2
derived, HallC3×C31×C79 ⋊ C22
HallC31×C79 ⋊ C2×D3
HallC3×C79 ⋊ C2×D31
HallC3×C31 ⋊ C2×D79
SylowC79 ⋊ C2×D93
SylowC31 ⋊ C2×D237
SylowC3 ⋊ C2×D2449

Subgroups

subgroupG/H
center, hypercenterC2D7347
commutator, cosocle, hypocenterC3×C31×C79C22
FrattiniC1G
Fitting, socleC2×C3×C31×C79C2
LCSG ▷ C3×C31×C79
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 115
transitive degreeμt(G) = 14694

A minimal faithful permutation representation — 2 generators on 115 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(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)(38,115)(39,114)(40,113)(41,112)(42,111)(43,110)(44,109)(45,108)(46,107)(47,106)(48,105)(49,104)(50,103)(51,102)(52,101)(53,100)(54,99)(55,98)(56,97)(57,96)(58,95)(59,94)(60,93)(61,92)(62,91)(63,90)(64,89)(65,88)(66,87)(67,86)(68,85)(69,84)(70,83)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77)

Conjugacy classes & character table

7350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD29388
maximal normal subgroup ofD29388
maximal quotient ofDic14694, D29388

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29388, 64);