C₄₁×#1181 #18011699

order	4756
isoclinism	isoclinic class of #1181
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₄₁×#1181

Splittings

Fitting, socle, Hall	C₂₉×C₄₁ ⋊ C₄
derived, Sylow	C₂₉ ⋊ C₄×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	#1181
commutator, hypocenter	C₂₉	C₄×C₄₁
Frattini	C₁	G
Fitting, socle	C₂₉×C₄₁	C₄
prime radical	C₄₁×D₂₉	C₂
cosocle	D₂₉	C₂×C₄₁
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₄₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 1189

A minimal faithful permutation representation — 2 generators on 70 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₄₁×#1181, C₄₁×C₃⋊#1181, #1181×C₄₁⋊C₅, …
maximal normal subgroup of	C₃×C₄₁×#1181, #1181×C₄₁⋊C₅, C₅×C₄₁×#1181, …
maximal quotient of	C₃×C₄₁×#1181, C₄₁×C₃⋊#1181, C₅×C₄₁×#1181, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4756, 7);

C41×#1181 #18011699