Dic₂₈₄₇ #26015644

order	11388
automorphism	Aut(G) order 9839232
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₂₈₄₇
unambiguous semidirect product	C₃⋊Dic₉₄₉

Splittings

derived, Hall	C₃×C₁₃×C₇₃ ⋊ C₄
Hall	C₁₃×C₇₃ ⋊ Dic₃
Hall	C₃×C₇₃ ⋊ Dic₁₃
Sylow	C₇₃ ⋊ Dic₃₉
Hall	C₃×C₁₃ ⋊ Dic₇₃
Sylow	C₁₃ ⋊ Dic₂₁₉
Sylow	C₃ ⋊ Dic₉₄₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₈₄₇
commutator, hypocenter	C₃×C₁₃×C₇₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₃×C₇₃	C₂
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 11388

A minimal faithful permutation representation — 2 generators on 93 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);(1,3,2,4)(6,7)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(22,93)(23,92)(24,91)(25,90)(26,89)(27,88)(28,87)(29,86)(30,85)(31,84)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(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:

2,3,13,73,2|a^2=e,b^a=b^2,c^a=c^12,d^a=d^72

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₈₅₄₁, C₃⋊#26015655, C₃⋊#26015656, …
maximal normal subgroup of	C₃⋊#26015655, C₃⋊#26015656, C₃⋊#26015654, …
maximal quotient of	Dic₈₅₄₁, C₃⋊Dic₂₈₄₇, C₃×Dic₂₈₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11388, 12);

Dic2847 #26015644