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C2×D7719 #44525272

order30876
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15438
direct productC2×D7719
unambiguous semidirect product(C2×C3)⋊D2573
unambiguous semidirect product(C2×C31)⋊D249
unambiguous semidirect product(C2×C83)⋊D93

Splittings

Fitting, socleC2×C3×C31×C83 ⋊ C2
derived, HallC3×C31×C83 ⋊ C22
HallC31×C83 ⋊ C2×D3
HallC3×C83 ⋊ C2×D31
HallC3×C31 ⋊ C2×D83
SylowC83 ⋊ C2×D93
SylowC31 ⋊ C2×D249
SylowC3 ⋊ C2×D2573

Subgroups

subgroupG/H
center, hypercenterC2D7719
commutator, cosocle, hypocenterC3×C31×C83C22
FrattiniC1G
Fitting, socleC2×C3×C31×C83C2
LCSG ▷ C3×C31×C83
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 119
transitive degreeμt(G) = 15438

A minimal faithful permutation representation — 2 generators on 119 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(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)(38,119)(39,118)(40,117)(41,116)(42,115)(43,114)(44,113)(45,112)(46,111)(47,110)(48,109)(49,108)(50,107)(51,106)(52,105)(53,104)(54,103)(55,102)(56,101)(57,100)(58,99)(59,98)(60,97)(61,96)(62,95)(63,94)(64,93)(65,92)(66,91)(67,90)(68,89)(69,88)(70,87)(71,86)(72,85)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)

Conjugacy classes & character table

7722 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30876
maximal normal subgroup ofD30876
maximal quotient ofDic15438, D30876

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30876, 34);