C₄₃×#436 #14582467

order	2752
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₄₃×#436

Subgroups

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂³
commutator	C₂²	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄	C₂³×C₄₃
socle	C₂²×C₄₃	C₂²×C₄
prime radical	C₂×D₄×C₄₃	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ G

122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1376

A minimal faithful permutation representation — 3 generators on 55 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)(48,49,52,50,51,53,55,54);(45,47)(49,53)(50,54);(48,50,52,53,51,54,55,49)

Conjugacy classes & character table

1204 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₃×#1330, C₄₃×#1581, C₄₃×#1583, …
maximal normal subgroup of	C₄₃×#1330, C₄₃×#1581, C₄₃×#1583, …
maximal quotient of	C₄₃×#1589, C₄₃×#1590, C₄₃×#1591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 117);

C43×#436 #14582467