D₄₁×D₄₁⋊C₅ #46777414

order	33620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₄₁×D₄₁⋊C₅
unambiguous semidirect product	D₄₁⋊(C₅×D₄₁)
unambiguous semidirect product	(C₄₁×D₄₁⋊C₅)⋊C₂
unambiguous semidirect product	((C₄₁⋊C₅)⋊D₄₁)⋊C₂
unambiguous semidirect product	(D₄₁×C₄₁⋊C₅)⋊C₂

Splittings

Fitting, socle, derived, Sylow	C₄₁² ⋊ C₂²×C₅
Hall	C₄₁×C₄₁⋊C₅ ⋊ C₂²
Hall	D₄₁² ⋊ C₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₁²	C₂²×C₅
LCS	G ▷ C₄₁²
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 410

A minimal faithful permutation representation — 2 generators on 82 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33620, 49);

D41×D41⋊C5 #46777414