C₁₉×#2249 #14560106

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#2249

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1216

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)(21,23)(24,25)(26,34)(27,39)(28,31)(29,42)(30,36)(32,35)(33,40)(37,46)(38,53)(41,54)(43,52)(44,55)(45,50)(47,49)(48,51);(24,26,35,49,29,38,41,52,28,37,50,55,40,51,27,36)(25,30,39,48,33,44,45,46,31,43,54,53,42,47,32,34);(20,21,22,23)(25,31)(30,43)(32,45)(33,42)(34,46)(39,54)(44,47)(48,53)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7446, C₁₉×#7447, C₁₉×#13689, …
maximal normal subgroup of	C₁₉×#7446, C₁₉×#7447, C₁₉×#13689, …
maximal quotient of	C₁₉×#12503, C₁₉×#12504, C₁₉×#12505, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 981);