C₃×#16864282 #27166159

order	12876
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×#16864282

Splittings

Fitting, socle, Hall	C₃×C₂₉×C₃₇ ⋊ C₄
derived, Hall	C₂₉×C₃₇ ⋊ C₃×C₄
Hall	C₃×C₃₇ ⋊ #1181
Hall	C₃×C₂₉ ⋊ Dic₃₇
Sylow	C₃₇ ⋊ C₃×#1181
Sylow	C₂₉ ⋊ C₃×Dic₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃	#16864282
commutator, hypocenter	C₂₉×C₃₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₃₇	C₄
prime radical	C₃×C₃₇×D₂₉	C₂
cosocle	C₃₇×D₂₉	C₂×C₃
LCS	G ▷ C₂₉×C₃₇
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 3219

A minimal faithful permutation representation — 2 generators on 69 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#50311130, C₉×#16864282, C₃×#16864282⋊C₃, …
maximal normal subgroup of	#50311130, C₉×#16864282, C₃×#16864282⋊C₃, …
maximal quotient of	C₉×#16864282, C₃²×#16864282, C₃×C₃⋊#16864282

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 28);

C3×#16864282 #27166159