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C2×D7553 #44475050

order30212
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15106
direct productC2×D7553
unambiguous semidirect product(C2×C7)⋊D1079
unambiguous semidirect product(C2×C13)⋊D581
unambiguous semidirect product(C2×C83)⋊D91

Splittings

Fitting, socleC2×C7×C13×C83 ⋊ C2
derived, HallC7×C13×C83 ⋊ C22
HallC13×C83 ⋊ C2×D7
HallC7×C83 ⋊ C2×D13
HallC7×C13 ⋊ C2×D83
SylowC83 ⋊ C2×D91
SylowC13 ⋊ C2×D581
SylowC7 ⋊ C2×D1079

Subgroups

subgroupG/H
center, hypercenterC2D7553
commutator, cosocle, hypocenterC7×C13×C83C22
FrattiniC1G
Fitting, socleC2×C7×C13×C83C2
LCSG ▷ C7×C13×C83
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 105
transitive degreeμt(G) = 15106

A minimal faithful permutation representation — 2 generators on 105 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);(4,9)(5,8)(6,7)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(24,105)(25,104)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

7556 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30212
maximal normal subgroup ofD30212
maximal quotient ofDic15106, D30212

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30212, 27);