C₂×C₁₉×#360 #14560001

order	2432
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₁₉×#360

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#102
commutator	C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

232 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 37
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(4,8,9,17)(5,11)(6,14)(10,12,15,18)(13,16);(3,4)(5,12)(6,15)(7,9)(8,16)(10,14)(11,17)(13,18)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₁₉×#360, C₁₉×#12650, C₁₉×#12735, …
maximal normal subgroup of	C₄×C₁₉×#360, C₁₉×#12650, C₁₉×#12735, …
maximal quotient of	C₂×C₁₉×#1333, C₂×C₁₉×#1334, C₁₉×#11598, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 876);