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C2×D4823 #34064402

order19292
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9646
direct productC2×D4823
unambiguous semidirect product(C2×C7)⋊D689
unambiguous semidirect product(C2×C13)⋊D371
unambiguous semidirect product(C2×C53)⋊D91

Splittings

Fitting, socleC2×C7×C13×C53 ⋊ C2
derived, HallC7×C13×C53 ⋊ C22
HallC13×C53 ⋊ C2×D7
HallC7×C53 ⋊ C2×D13
HallC7×C13 ⋊ C2×D53
SylowC53 ⋊ C2×D91
SylowC13 ⋊ C2×D371
SylowC7 ⋊ C2×D689

Subgroups

subgroupG/H
center, hypercenterC2D4823
commutator, cosocle, hypocenterC7×C13×C53C22
FrattiniC1G
Fitting, socleC2×C7×C13×C53C2
LCSG ▷ C7×C13×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 75
transitive degreeμt(G) = 9646

A minimal faithful permutation representation — 2 generators on 75 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);(4,9)(5,8)(6,7)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Conjugacy classes & character table

4826 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19292, C2×D14469
maximal normal subgroup ofD19292
maximal quotient ofDic9646, D19292, C2×D14469

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19292, 40);