C₂²⋊D₁₇ #3629

order	136
isoclinism	isoclinic class of Dic₃₄
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₇) (order 1088) · Inn(G) = C₂×D₁₇ · Out(G) = C₁₆
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

C₂²⋊D₁₇

Fitting	C₂²×C₁₇ ⋊ C₂
Sylow	C₁₇ ⋊ D₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 68

A minimal faithful permutation representation — 2 generators on 21 points:

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

Polycyclic presentation:

2^3,17|b^a=bc,d^a=d^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(136, 8);