Finite Group Databasebeta

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Cayley diagram

D253 #92783

order506
isoclinismisoclinic class of D253
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD253
unambiguous semidirect productC11⋊D23
unambiguous semidirect productC23⋊D11

Splittings

Fitting, socle, derived, HallC11×C23 ⋊ C2
SylowC23 ⋊ D11
SylowC11 ⋊ D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C23C2
LCSG ▷ C11×C23
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 253

A minimal faithful permutation representation — 2 generators on 34 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Polycyclic presentation:

2,11,23|b^a=b^10,c^a=c^22

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D23, C2×D253, C3×D253, …
maximal normal subgroup ofD11×D23, C2×D253, C3×D253, …
maximal quotient ofDic253, C2×D253, C3×D253, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(506, 5);