C₄₇×#433 #15688688

order	3008
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₄₇×#433

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 3 generators on 71 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)(50,53)(51,52)(54,55)(56,57,59,62,60,63,66,69)(58,61,65,68,64,67,70,71);(49,52)(53,55)(56,58)(57,61)(59,65)(60,64)(62,68)(63,67)(66,70)(69,71);(48,50,51,54)(49,53,52,55)(58,64)(61,67)(65,70)(68,71)

Conjugacy classes & character table

1316 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄₇×#433, C₄₇×#2921, C₄₇×#2922, …
maximal normal subgroup of	C₂×C₄₇×#433, C₄₇×#2921, C₄₇×#2922, …
maximal quotient of	C₄₇×#1746, C₄₇×#1750, C₄₇×#1768, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 114);

C47×#433 #15688688