C₁₉×#12778 #18018737

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12778
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#12778

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1790
commutator	C₂×Q₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×#41	C₂³×C₁₉
prime radical	C₁₉×#3549	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

860 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 860 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5766);