C₄₇×#553 #15688808

order	3008
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₄₇×#553

Subgroups

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

238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 4 generators on 63 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)(54,55)(57,60)(61,62);(49,53)(51,54)(56,57,59,60)(58,62,63,61);(48,50)(49,54)(51,53)(52,55);(48,51,52,54)(49,50,53,55)(56,58,59,63)(57,61,60,62)

Conjugacy classes & character table

1175 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#3297, C₄₇×#3301, C₄₇×#3307, …
maximal normal subgroup of	C₄₇×#3297, C₄₇×#3301, C₄₇×#3307, …
maximal quotient of	C₄₇×#2345, C₄₇×#2347, C₄₇×#2352, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 234);

C47×#553 #15688808