C₄₁×#552 #14580020

order	2624
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₄₁×#552

Subgroups

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₄₁
prime radical	C₂×D₄×C₄₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ G

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1312

A minimal faithful permutation representation — 4 generators on 57 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)(42,43,46,47)(44,45,48,49)(52,56)(54,57);(43,47)(45,49)(50,51,53,55)(52,54,56,57);(42,44,46,48)(43,45,47,49)(50,52)(51,54)(53,56)(55,57);(42,45)(43,48)(44,47)(46,49)

Conjugacy classes & character table

1025 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₁×#3296, C₄₁×#3300, C₄₁×#3310, …
maximal normal subgroup of	C₄₁×#3296, C₄₁×#3300, C₄₁×#3310, …
maximal quotient of	C₄₁×#2343, C₄₁×#2344, C₄₁×#2346, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 233);

C41×#552 #14580020