D₁₁₉₂₅ #37558679

order	23850
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₉₂₅
unambiguous semidirect product	C₉⋊D₁₃₂₅
unambiguous semidirect product	C₂₅⋊D₄₇₇
unambiguous semidirect product	C₅₃⋊D₂₂₅

Splittings

Fitting, derived, Hall	C₉×C₂₅×C₅₃ ⋊ C₂
Hall	C₂₅×C₅₃ ⋊ D₉
Hall	C₉×C₅₃ ⋊ D₂₅
Hall	C₉×C₂₅ ⋊ D₅₃
Sylow	C₅₃ ⋊ D₂₂₅
Sylow	C₂₅ ⋊ D₄₇₇
Sylow	C₉ ⋊ D₁₃₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₅×C₅₃	C₂
Frattini	C₃×C₅	D₇₉₅
socle	C₃×C₅×C₅₃	D₁₅
LCS	G ▷ C₉×C₂₅×C₅₃
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 11925

A minimal faithful permutation representation — 2 generators on 87 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);(2,9)(3,8)(4,7)(5,6)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Polycyclic presentation:

2,3,5,53,3,5|b^3=e^2,c^5=f^4,b^a=b^2e,c^a=c^4f,d^a=d^52,e^a=e^2,f^a=f^4

Conjugacy classes & character table

5964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23850, 8);

D11925 #37558679