Finite Group Databasebeta

← Prev (#37564625) Next (#37564627) →

C2×D6061 #37564626

order24244
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12122
direct productC2×D6061
unambiguous semidirect product(C2×C11)⋊D551
unambiguous semidirect product(C2×C19)⋊D319
unambiguous semidirect product(C2×C29)⋊D209

Splittings

Fitting, socleC2×C11×C19×C29 ⋊ C2
derived, HallC11×C19×C29 ⋊ C22
HallC19×C29 ⋊ C2×D11
HallC11×C29 ⋊ C2×D19
HallC11×C19 ⋊ C2×D29
SylowC29 ⋊ C2×D209
SylowC19 ⋊ C2×D319
SylowC11 ⋊ C2×D551

Subgroups

subgroupG/H
center, hypercenterC2D6061
commutator, cosocle, hypocenterC11×C19×C29C22
FrattiniC1G
Fitting, socleC2×C11×C19×C29C2
LCSG ▷ C11×C19×C29
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 12122

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);(4,13)(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)(34,61)(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

6064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD24244
maximal normal subgroup ofD24244
maximal quotient ofDic12122, D24244

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24244, 27);