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C2×D7667 #44501544

order30668
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15334
direct productC2×D7667
unambiguous semidirect product(C2×C11)⋊D697
unambiguous semidirect product(C2×C17)⋊D451
unambiguous semidirect product(C2×C41)⋊D187

Splittings

Fitting, socleC2×C11×C17×C41 ⋊ C2
derived, HallC11×C17×C41 ⋊ C22
HallC17×C41 ⋊ C2×D11
HallC11×C41 ⋊ C2×D17
HallC11×C17 ⋊ C2×D41
SylowC41 ⋊ C2×D187
SylowC17 ⋊ C2×D451
SylowC11 ⋊ C2×D697

Subgroups

subgroupG/H
center, hypercenterC2D7667
commutator, cosocle, hypocenterC11×C17×C41C22
FrattiniC1G
Fitting, socleC2×C11×C17×C41C2
LCSG ▷ C11×C17×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 71
transitive degreeμt(G) = 15334

A minimal faithful permutation representation — 2 generators on 71 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

7670 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30668
maximal normal subgroup ofD30668
maximal quotient ofDic15334, D30668

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30668, 35);