C₃×#22551381 #37590248

order	24642
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×#22551381

Splittings

Fitting, socle	C₃×C₃₇² ⋊ D₃
derived	#16861552 ⋊ C₂×C₃
Hall	C₃×#16861552 ⋊ C₂
Sylow	C₃₇² ⋊ C₃×D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	#22551381
commutator, cosocle, hypocenter	#16861552	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₃₇²	D₃
LCS	G ▷ #16861552
UCS	C₁ ◁ C₃

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 222

A minimal faithful permutation representation — 2 generators on 77 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24642, 68);

C3×#22551381 #37590248