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C2×D4991 #34093196

order19964
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9982
direct productC2×D4991
unambiguous semidirect product(C2×C7)⋊D713
unambiguous semidirect product(C2×C23)⋊D217
unambiguous semidirect product(C2×C31)⋊D161

Splittings

Fitting, socleC2×C7×C23×C31 ⋊ C2
derived, HallC7×C23×C31 ⋊ C22
HallC23×C31 ⋊ C2×D7
HallC7×C31 ⋊ C2×D23
HallC7×C23 ⋊ C2×D31
SylowC31 ⋊ C2×D161
SylowC23 ⋊ C2×D217
SylowC7 ⋊ C2×D713

Subgroups

subgroupG/H
center, hypercenterC2D4991
commutator, cosocle, hypocenterC7×C23×C31C22
FrattiniC1G
Fitting, socleC2×C7×C23×C31C2
LCSG ▷ C7×C23×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 9982

A minimal faithful permutation representation — 2 generators on 63 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);(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)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

4994 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19964, C2×D14973
maximal normal subgroup ofD19964
maximal quotient ofDic9982, D19964, C2×D14973

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19964, 17);