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C2×D7733 #44525835

order30932
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15466
direct productC2×D7733
unambiguous semidirect product(C2×C11)⋊D703
unambiguous semidirect product(C2×C19)⋊D407
unambiguous semidirect product(C2×C37)⋊D209

Splittings

Fitting, socleC2×C11×C19×C37 ⋊ C2
derived, HallC11×C19×C37 ⋊ C22
HallC19×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D19
HallC11×C19 ⋊ C2×D37
SylowC37 ⋊ C2×D209
SylowC19 ⋊ C2×D407
SylowC11 ⋊ C2×D703

Subgroups

subgroupG/H
center, hypercenterC2D7733
commutator, cosocle, hypocenterC11×C19×C37C22
FrattiniC1G
Fitting, socleC2×C11×C19×C37C2
LCSG ▷ C11×C19×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 15466

A minimal faithful permutation representation — 2 generators on 69 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(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

7736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30932
maximal normal subgroup ofD30932
maximal quotient ofDic15466, D30932

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30932, 27);