C₂⁴×D₁₃ #88267

order	416
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product	C₂⁴×D₁₃
unambiguous semidirect product	C₁₃⋊C₂⁵
unambiguous semidirect product	(C₂×C₁₃)⋊C₂⁴

Fitting, socle	C₂⁴×C₁₃ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂⁵

	subgroup	G/H
center, hypercenter	C₂⁴	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁴

748 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 5 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 234);