D₁₂₅₂₉ #38736799

order	25058
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₅₂₉
unambiguous semidirect product	C₁₁⋊D₁₁₃₉
unambiguous semidirect product	C₁₇⋊D₇₃₇
unambiguous semidirect product	C₆₇⋊D₁₈₇

Splittings

Fitting, socle, derived, Hall	C₁₁×C₁₇×C₆₇ ⋊ C₂
Hall	C₁₇×C₆₇ ⋊ D₁₁
Hall	C₁₁×C₆₇ ⋊ D₁₇
Hall	C₁₁×C₁₇ ⋊ D₆₇
Sylow	C₆₇ ⋊ D₁₈₇
Sylow	C₁₇ ⋊ D₇₃₇
Sylow	C₁₁ ⋊ D₁₁₃₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₇×C₆₇	C₂
LCS	G ▷ C₁₁×C₁₇×C₆₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 12529

A minimal faithful permutation representation — 2 generators on 95 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)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(2,11)(3,10)(4,9)(5,8)(6,7)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(30,95)(31,94)(32,93)(33,92)(34,91)(35,90)(36,89)(37,88)(38,87)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81)(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)

Polycyclic presentation:

2,11,17,67|b^a=b^10,c^a=c^16,d^a=d^66

Conjugacy classes & character table

6266 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₂₅₂₉
maximal normal subgroup of	C₂×D₁₂₅₂₉
maximal quotient of	Dic₁₂₅₂₉, C₂×D₁₂₅₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25058, 9);

D12529 #38736799