C₇×C₃₁×D₂₉ #27160406

order	12586
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇×C₃₁×D₂₉

Splittings

Fitting, socle, Hall	C₇×C₂₉×C₃₁ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₇×C₃₁
Hall	C₂₉×C₃₁ ⋊ C₂×C₇
Hall	C₇×C₂₉ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₃₁	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₇×C₂₉×C₃₁	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₇×C₃₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 6293

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

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₃₁×#1181, C₇×C₃₁⋊#1181, C₇×D₂₉×D₃₁, …
maximal normal subgroup of	C₇×C₃₁×#1181, C₇×C₃₁⋊#1181, C₇×D₂₉×D₃₁, …
maximal quotient of	C₇×C₃₁×Dic₂₉, C₂×C₇×C₃₁×D₂₉, C₃×C₇×C₃₁×D₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12586, 4);

C7×C31×D29 #27160406