C₂×C₅×C₄₃² #32914945

order	18490
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄₃

Aliases

abelian

C₂×C₅×C₄₃²

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 18490

A minimal faithful permutation representation — 2 generators on 93 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93)

Conjugacy classes & character table

18490 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₄₃⋊Dic₂₁₅, C₄₃×Dic₂₁₅, Dic₅×C₄₃², …
socle of	C₄×C₅×C₄₃², C₄₃⋊Dic₂₁₅, C₄₃×Dic₂₁₅, …
maximal subgroup of	C₄×C₅×C₄₃², C₄₃⋊Dic₂₁₅, C₄₃×Dic₂₁₅, …
maximal normal subgroup of	C₄×C₅×C₄₃², C₄₃⋊Dic₂₁₅, C₄₃×Dic₂₁₅, …
maximal quotient of	C₄×C₅×C₄₃², C₂²×C₅×C₄₃²

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18490, 5);

C2×C5×C432 #32914945