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C2×D6063 #37564664

order24252
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12126
direct productC2×D6063
unambiguous semidirect product(C2×C3)⋊D2021
unambiguous semidirect product(C2×C43)⋊D141
unambiguous semidirect product(C2×C47)⋊D129

Splittings

Fitting, socleC2×C3×C43×C47 ⋊ C2
derived, HallC3×C43×C47 ⋊ C22
HallC43×C47 ⋊ C2×D3
HallC3×C47 ⋊ C2×D43
HallC3×C43 ⋊ C2×D47
SylowC47 ⋊ C2×D129
SylowC43 ⋊ C2×D141
SylowC3 ⋊ C2×D2021

Subgroups

subgroupG/H
center, hypercenterC2D6063
commutator, cosocle, hypocenterC3×C43×C47C22
FrattiniC1G
Fitting, socleC2×C3×C43×C47C2
LCSG ▷ C3×C43×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 12126

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

Conjugacy classes & character table

6066 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD24252
maximal normal subgroup ofD24252
maximal quotient ofDic12126, D24252

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24252, 34);