C₄₇×#386 #15688641

order	3008
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄₇×#386

Subgroups

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂³
commutator	C₂²	C₂²×C₄×C₄₇
Frattini, cosocle	C₂³	C₂³×C₄₇
prime radical	C₂²×D₄×C₄₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

286 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 106 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)(52,53,54,55)(57,59);(52,53)(54,55)(56,57,58,59);(48,49)(50,51)(52,53)(54,55)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#1390, C₄₇×#1790, C₄₇×#1867, …
maximal normal subgroup of	C₄₇×#1390, C₄₇×#1790, C₄₇×#1867, …
maximal quotient of	C₄₇×C₂²⋊#95, C₄₇×#1436, C₄₇×#1437, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 67);