#467×C₆₇ #16862995

order	4288
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#467×C₆₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₆₇
prime radical	C₂³×C₆₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 2144

A minimal faithful permutation representation — 3 generators on 87 points:

(1,2)(3,4)(5,6,9,12)(7,13,16,20)(8,17,14,11)(10,18,19,15)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(5,7,14,18,9,16,8,15)(6,10,17,20,12,19,11,13);(2,4)

Conjugacy classes & character table

1474 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₆₇×#1348, C₆₇×#1350, C₆₇×#2187, …
maximal normal subgroup of	C₆₇×#1348, C₆₇×#1350, C₆₇×#2187, …
maximal quotient of	C₆₇×#1669, C₆₇×#1670, C₆₇×#1675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4288, 148);

#467×C67 #16862995