C₄₇×#535 #15688790

order	3008
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₄₇×#535

Subgroups

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₄₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ G

334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 59
transitive degree	μ_t(G) = 752

A minimal faithful permutation representation — 4 generators on 59 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)(49,51)(53,56)(54,58);(52,53,55,56)(54,57,58,59);(48,49)(50,51)(52,53)(54,57)(55,56)(58,59);(52,54)(53,57)(55,58)(56,59)

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#1910, C₄₇×#1911, C₄₇×#1914, …
maximal normal subgroup of	C₄₇×#1910, C₄₇×#1911, C₄₇×#1914, …
maximal quotient of	C₄₇×#2309, C₄₇×#2311, C₄₇×#2317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 216);