C₄₇×#388 #15688643

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

Aliases

direct product

C₄₇×#388

Subgroups

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

190 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 90 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 — 3 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)(53,54)(56,57,59,58);(52,53,55,54)(56,58,59,57);(48,49)(50,51)(52,54,55,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₄₇×#388, C₄₇×#2290, C₄₇×#2293, …
maximal normal subgroup of	C₂×C₄₇×#388, C₄₇×#2290, C₄₇×#2293, …
maximal quotient of	C₄₇×#1434, C₄₇×#1436, C₄₇×#1437, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 69);