C₁₉×#11412 #18017371

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₉×#11412

Subgroups

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

260 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 190 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,26,24,27,30,33)(22,25,29,32,28,31,34,35)(36,37)(38,42)(39,44)(40,45)(41,43)(46,53)(47,54)(48,52)(49,57)(50,55)(51,56)(58,64)(59,62)(60,63)(61,65)(66,67);(20,22)(21,25)(23,29)(24,28)(26,32)(27,31)(30,34)(33,35)(36,38,39,46,40,47,49,58,41,48,50,59,51,60,61,66)(37,42,44,53,45,54,57,64,43,52,55,62,56,63,65,67);(22,28)(25,31)(29,34)(32,35)(37,43)(42,52)(44,55)(45,56)(53,62)(54,63)(57,65)(64,67)

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4400);