C₄⋊C₁₆×C₇₁ #17985494

order	4544
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄⋊C₁₆×C₇₁
unambiguous semidirect product	C₄⋊(C₁₆×C₇₁)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₇₁	C₂²
commutator	C₂	C₂×C₁₆×C₇₁
Frattini, cosocle	C₂×C₈	C₂²×C₇₁
socle, prime radical	C₂²×C₇₁	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₇₁ ◁ G

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 4544

A minimal faithful permutation representation — 2 generators on 91 points:

(2,4)(5,6,7,10,8,11,13,16,9,12,14,17,15,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2,3,4)

Conjugacy classes & character table

2840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×D₄⋊C₁₆, C₇₁×#1330, C₇₁×Q₈⋊C₁₆, …
maximal normal subgroup of	C₇₁×D₄⋊C₁₆, C₇₁×#1330, C₇₁×Q₈⋊C₁₆, …
maximal quotient of	C₇₁×#1367, C₇₁×#1370, C₇₁×#1374, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 44);

C4⋊C16×C71 #17985494