C₄₇×#520 #15688775

order	3008
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₄₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄₇×#520

Subgroups

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂⁴
commutator	C₂	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²	C₂⁴×C₄₇
prime radical	C₂×#41×C₄₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 1504

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)(48,49,50,51)(52,53)(54,58)(55,56)(57,59);(53,56)(57,58);(52,53)(54,57)(55,56)(58,59);(52,54,55,59)(53,57,56,58)

Conjugacy classes & character table

1598 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#1859, C₄₇×#1860, C₄₇×#1882, …
maximal normal subgroup of	C₄₇×#1859, C₄₇×#1860, C₄₇×#1882, …
maximal quotient of	C₄₇×#2274, C₄₇×#2275, C₄₇×#2276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 201);

C47×#520 #15688775