C₄₇×#547 #15688802

order	3008
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄₇×#547

Subgroups

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

292 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 166 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) = 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)(49,51)(52,53,56,57)(54,55,58,59);(53,57)(55,59);(48,49)(50,51)(52,54,56,58)(53,55,57,59);(52,55)(53,58)(54,57)(56,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#1625, C₄₇×#1635, C₄₇×#1647, …
maximal normal subgroup of	C₄₇×#1625, C₄₇×#1635, C₄₇×#1647, …
maximal quotient of	C₄₇×#2339, C₄₇×#2344, D₄×C₄⋊C₄×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 228);