Dic₂₃₁ #11745110

order	924
isoclinism	isoclinic class of D₂₃₁
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₂₃₁
unambiguous semidirect product	C₃⋊Dic₇₇
unambiguous semidirect product	C₇⋊Dic₃₃
unambiguous semidirect product	C₁₁⋊Dic₂₁

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₃₁
commutator, hypocenter	C₃×C₇×C₁₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇×C₁₁	C₂
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 924

A minimal faithful permutation representation — 2 generators on 25 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);(1,3,2,4)(6,7)(9,14)(10,13)(11,12)(16,25)(17,24)(18,23)(19,22)(20,21)

Polycyclic presentation:

2^2,3,7,11|a^2=b,c^a=c^2,d^a=d^6,e^a=e^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(924, 11);