Dic₆₂₃₅ #38735539

order	24940
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₆₂₃₅
unambiguous semidirect product	C₄₃⋊Dic₁₄₅

Splittings

derived, Hall	C₅×C₂₉×C₄₃ ⋊ C₄
Hall	C₂₉×C₄₃ ⋊ Dic₅
Hall	C₅×C₄₃ ⋊ Dic₂₉
Hall	C₅×C₂₉ ⋊ Dic₄₃
Sylow	C₄₃ ⋊ Dic₁₄₅
Sylow	C₂₉ ⋊ Dic₂₁₅
Sylow	C₅ ⋊ Dic₁₂₄₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₂₃₅
commutator, hypocenter	C₅×C₂₉×C₄₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₂₉×C₄₃	C₂
LCS	G ▷ C₅×C₂₉×C₄₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 24940

A minimal faithful permutation representation — 2 generators on 81 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);(1,3,2,4)(6,9)(7,8)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Polycyclic presentation:

2,5,29,43,2|a^2=e,b^a=b^4,c^a=c^28,d^a=d^42

Conjugacy classes & character table

6238 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₂₄₇₀
maximal normal subgroup of	Dic₁₂₄₇₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24940, 8);

Dic6235 #38735539