Finite Group Databasebeta

← Prev (#37550865) Next (#37550867) →

C2×D5797 #37550866

order23188
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11594
direct productC2×D5797
unambiguous semidirect product(C2×C11)⋊D527
unambiguous semidirect product(C2×C17)⋊D341
unambiguous semidirect product(C2×C31)⋊D187

Splittings

Fitting, socleC2×C11×C17×C31 ⋊ C2
derived, HallC11×C17×C31 ⋊ C22
HallC17×C31 ⋊ C2×D11
HallC11×C31 ⋊ C2×D17
HallC11×C17 ⋊ C2×D31
SylowC31 ⋊ C2×D187
SylowC17 ⋊ C2×D341
SylowC11 ⋊ C2×D527

Subgroups

subgroupG/H
center, hypercenterC2D5797
commutator, cosocle, hypocenterC11×C17×C31C22
FrattiniC1G
Fitting, socleC2×C11×C17×C31C2
LCSG ▷ C11×C17×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 11594

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)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,61)(33,60)(34,59)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(43,50)(44,49)(45,48)(46,47)

Conjugacy classes & character table

5800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23188
maximal normal subgroup ofD23188
maximal quotient ofDic11594, D23188

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23188, 27);