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C2×D4945 #34089922

order19780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9890
direct productC2×D4945
unambiguous semidirect product(C2×C5)⋊D989
unambiguous semidirect product(C2×C23)⋊D215
unambiguous semidirect product(C2×C43)⋊D115

Splittings

Fitting, socleC2×C5×C23×C43 ⋊ C2
derived, HallC5×C23×C43 ⋊ C22
HallC23×C43 ⋊ C2×D5
HallC5×C43 ⋊ C2×D23
HallC5×C23 ⋊ C2×D43
SylowC43 ⋊ C2×D115
SylowC23 ⋊ C2×D215
SylowC5 ⋊ C2×D989

Subgroups

subgroupG/H
center, hypercenterC2D4945
commutator, cosocle, hypocenterC5×C23×C43C22
FrattiniC1G
Fitting, socleC2×C5×C23×C43C2
LCSG ▷ C5×C23×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 9890

A minimal faithful permutation representation — 2 generators on 73 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);(4,7)(5,6)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

4948 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19780, C2×D14835
maximal normal subgroup ofD19780
maximal quotient ofDic9890, D19780, C2×D14835

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19780, 21);