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C2×D4669 #32916385

order18676
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9338
direct productC2×D4669
unambiguous semidirect product(C2×C7)⋊D667
unambiguous semidirect product(C2×C23)⋊D203
unambiguous semidirect product(C2×C29)⋊D161

Splittings

Fitting, socleC2×C7×C23×C29 ⋊ C2
derived, HallC7×C23×C29 ⋊ C22
HallC23×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×D23
HallC7×C23 ⋊ C2×D29
SylowC29 ⋊ C2×D161
SylowC23 ⋊ C2×D203
SylowC7 ⋊ C2×D667

Subgroups

subgroupG/H
center, hypercenterC2D4669
commutator, cosocle, hypocenterC7×C23×C29C22
FrattiniC1G
Fitting, socleC2×C7×C23×C29C2
LCSG ▷ C7×C23×C29
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 9338

A minimal faithful permutation representation — 2 generators on 61 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);(4,9)(5,8)(6,7)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)

Conjugacy classes & character table

4672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18676, C2×D14007
maximal normal subgroup ofD18676
maximal quotient ofDic9338, D18676, C2×D14007

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18676, 32);