Dic₈₇₈₉ #47975868

order	35156
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₈₇₈₉
unambiguous semidirect product	C₁₁⋊Dic₇₉₉
unambiguous semidirect product	C₄₇⋊Dic₁₈₇

Splittings

derived, Hall	C₁₁×C₁₇×C₄₇ ⋊ C₄
Hall	C₁₇×C₄₇ ⋊ Dic₁₁
Hall	C₁₁×C₄₇ ⋊ Dic₁₇
Hall	C₁₁×C₁₇ ⋊ Dic₄₇
Sylow	C₄₇ ⋊ Dic₁₈₇
Sylow	C₁₇ ⋊ Dic₅₁₇
Sylow	C₁₁ ⋊ Dic₇₉₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₇₈₉
commutator, hypocenter	C₁₁×C₁₇×C₄₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₇×C₄₇	C₂
LCS	G ▷ C₁₁×C₁₇×C₄₇
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 35156

A minimal faithful permutation representation — 2 generators on 79 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(34,79)(35,78)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57)

Polycyclic presentation:

2,11,17,47,2|a^2=e,b^a=b^10,c^a=c^16,d^a=d^46

Conjugacy classes & character table

8792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35156, 8);

Dic8789 #47975868