Finite Group Databasebeta

← Prev (#44526399) Next (#44526401) →

C2×D7743 #44526400

order30972
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15486
direct productC2×D7743
unambiguous semidirect product(C2×C3)⋊D2581
unambiguous semidirect product(C2×C29)⋊D267
unambiguous semidirect product(C2×C89)⋊D87

Splittings

Fitting, socleC2×C3×C29×C89 ⋊ C2
derived, HallC3×C29×C89 ⋊ C22
HallC29×C89 ⋊ C2×D3
HallC3×C89 ⋊ C2×D29
SylowC89 ⋊ C2×D87
HallC3×C29 ⋊ C2×D89
SylowC29 ⋊ C2×D267
SylowC3 ⋊ C2×D2581

Subgroups

subgroupG/H
center, hypercenterC2D7743
commutator, cosocle, hypocenterC3×C29×C89C22
FrattiniC1G
Fitting, socleC2×C3×C29×C89C2
LCSG ▷ C3×C29×C89
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 123
transitive degreeμt(G) = 15486

A minimal faithful permutation representation — 2 generators on 123 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(4,5)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,123)(37,122)(38,121)(39,120)(40,119)(41,118)(42,117)(43,116)(44,115)(45,114)(46,113)(47,112)(48,111)(49,110)(50,109)(51,108)(52,107)(53,106)(54,105)(55,104)(56,103)(57,102)(58,101)(59,100)(60,99)(61,98)(62,97)(63,96)(64,95)(65,94)(66,93)(67,92)(68,91)(69,90)(70,89)(71,88)(72,87)(73,86)(74,85)(75,84)(76,83)(77,82)(78,81)(79,80)

Conjugacy classes & character table

7746 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30972
maximal normal subgroup ofD30972
maximal quotient ofDic15486, D30972

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30972, 36);