Dic₈₄₈₇ #46800381

order	33948
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₈₄₈₇
unambiguous semidirect product	C₉⋊Dic₉₄₃
unambiguous semidirect product	C₂₃⋊Dic₃₆₉

Splittings

derived, Hall	C₉×C₂₃×C₄₁ ⋊ C₄
Hall	C₂₃×C₄₁ ⋊ Dic₉
Hall	C₉×C₄₁ ⋊ Dic₂₃
Hall	C₉×C₂₃ ⋊ Dic₄₁
Sylow	C₄₁ ⋊ Dic₂₀₇
Sylow	C₂₃ ⋊ Dic₃₆₉
Sylow	C₉ ⋊ Dic₉₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₄₈₇
commutator, hypocenter	C₉×C₂₃×C₄₁	C₄
Frattini	C₂×C₃	D₂₈₂₉
Fitting, cosocle	C₂×C₉×C₂₃×C₄₁	C₂
socle, prime radical	C₂×C₃×C₂₃×C₄₁	D₃
LCS	G ▷ C₉×C₂₃×C₄₁
UCS	C₁ ◁ C₂

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 33948

A minimal faithful permutation representation — 2 generators on 77 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)

Polycyclic presentation:

2,3,23,41,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=c^22,d^a=d^40,f^a=f^2

Conjugacy classes & character table

8490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33948, 8);

Dic8487 #46800381