Dic₅₈₈₃ #37555201

order	23532
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₅₈₈₃
unambiguous semidirect product	C₃⋊Dic₁₉₆₁

Splittings

derived, Hall	C₃×C₃₇×C₅₃ ⋊ C₄
Hall	C₃₇×C₅₃ ⋊ Dic₃
Hall	C₃×C₅₃ ⋊ Dic₃₇
Hall	C₃×C₃₇ ⋊ Dic₅₃
Sylow	C₅₃ ⋊ Dic₁₁₁
Sylow	C₃₇ ⋊ Dic₁₅₉
Sylow	C₃ ⋊ Dic₁₉₆₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅₈₈₃
commutator, hypocenter	C₃×C₃₇×C₅₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₃₇×C₅₃	C₂
LCS	G ▷ C₃×C₃₇×C₅₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 23532

A minimal faithful permutation representation — 2 generators on 97 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)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(1,3,2,4)(6,7)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(46,97)(47,96)(48,95)(49,94)(50,93)(51,92)(52,91)(53,90)(54,89)(55,88)(56,87)(57,86)(58,85)(59,84)(60,83)(61,82)(62,81)(63,80)(64,79)(65,78)(66,77)(67,76)(68,75)(69,74)(70,73)(71,72)

Polycyclic presentation:

2,3,37,53,2|a^2=e,b^a=b^2,c^a=c^36,d^a=d^52

Conjugacy classes & character table

5886 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₁₇₆₆
maximal normal subgroup of	Dic₁₁₇₆₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23532, 9);

Dic5883 #37555201