C₁₉×C₉₇ #14270403

order	1843
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₉×C₃₂ (order 1728) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₉×C₃₂
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₈₄₃
abelian	C₁₉×C₉₇

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 116
transitive degree	μ_t(G) = 1843

A minimal faithful permutation representation — 1 generator on 116 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116)

Conjugacy classes & character table

1843 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1843, 1);

center of	D₅×C₁₉×C₉₇, A₄×C₁₉×C₉₇, D₇×C₁₉×C₉₇, …
derived subgroup of	D₁₈₄₃, #30658671, #30658672, …
Fitting subgroup of	D₁₉×C₉₇, C₁₉×D₉₇, D₁₈₄₃, …
socle of	D₁₉×C₉₇, C₁₉×D₉₇, D₁₈₄₃, …
maximal subgroup of	D₁₉×C₉₇, C₁₉×D₉₇, D₁₈₄₃, …
maximal normal subgroup of	D₁₉×C₉₇, C₁₉×D₉₇, D₁₈₄₃, …
maximal quotient of	C₂×C₁₉×C₉₇, C₁₁×C₁₉×C₉₇, C₁₃×C₁₉×C₉₇, …

C19×C97 #14270403