C₂×#103×C₄₁ #14579883

order	2624
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×#103×C₄₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₁	D₄
commutator	C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄	C₂³×C₄₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 2624

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(3,4,5,6)(8,11)(9,13)(12,14);(7,8,10,12)(9,14,13,11)

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×#103×C₄₁, C₄₁×#1763, C₄₁×#1787, …
maximal normal subgroup of	C₄×#103×C₄₁, C₄₁×#1763, C₄₁×#1787, …
maximal quotient of	C₂×C₄₁×Q₈⋊C₈, C₄₁×#1481, C₄₁×#1487, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 96);

C2×#103×C41 #14579883