C₂×C₆₇×#3874 #34117239

order	20100
isoclinism	isoclinic class of #3874
automorphism	?
homology	Abelianization (H₁) = C₂²×C₆₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂×C₆₇×#3874

Splittings

Fitting, socle	C₂×C₅²×C₆₇ ⋊ D₃
derived, Hall	C₅²⋊C₃ ⋊ C₂²×C₆₇
Hall	C₆₇×C₅²⋊C₃ ⋊ C₂²
Hall	C₅²×C₆₇ ⋊ C₂×D₃
Sylow	C₅² ⋊ C₂×D₃×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₆₇	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂²×C₆₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₆₇	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂×C₆₇

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 84
transitive degree	μ_t(G) = 2010

A minimal faithful permutation representation — 2 generators on 84 points:

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

Conjugacy classes & character table

1742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 95);

C2×C67×#3874 #34117239