C₃×C₂₉×Dic₃₇ #27166134

order	12876
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₂₉×Dic₃₇

Splittings

derived, Sylow	C₃₇ ⋊ C₃×C₄×C₂₉
Hall	C₃×C₂₉×C₃₇ ⋊ C₄
Hall	C₂₉×C₃₇ ⋊ C₃×C₄
Hall	C₃×C₃₇ ⋊ C₄×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	D₃₇
commutator, hypocenter	C₃₇	C₃×C₄×C₂₉
Frattini	C₂	C₃×C₂₉×D₃₇
Fitting, socle, prime radical	C₂×C₃×C₂₉×C₃₇	C₂
cosocle	C₂×C₃₇	C₂×C₃×C₂₉
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₃×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 12876

A minimal faithful permutation representation — 2 generators on 73 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)(38,41,40,39)(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);(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)

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₉×Dic₃₇, C₂₉×#13050607, C₃×C₂₉×Dic₃₇⋊C₃, …
maximal normal subgroup of	C₉×C₂₉×Dic₃₇, C₂₉×#13050607, C₃×C₂₉×Dic₃₇⋊C₃, …
maximal quotient of	C₉×C₂₉×Dic₃₇, C₃×C₂₉×Dic₁₁₁, C₃²×C₂₉×Dic₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 3);

C3×C29×Dic37 #27166134