Dic₇₇ #64569

order	308
isoclinism	isoclinic class of D₇₇
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₇₇
unambiguous semidirect product	C₇⋊Dic₁₁
unambiguous semidirect product	C₁₁⋊Dic₇

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₇
commutator, hypocenter	C₇×C₁₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₁	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 308

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2)(3,4)(5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22);(1,3,2,4)(6,11)(7,10)(8,9)(13,22)(14,21)(15,20)(16,19)(17,18)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(308, 3);