C₇₁×D₈₇ #27136403

order	12354
isoclinism	isoclinic class of D₈₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₇₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇₁×D₈₇
unambiguous semidirect product	C₃⋊(D₂₉×C₇₁)
unambiguous semidirect product	C₂₉⋊(D₃×C₇₁)

Splittings

Fitting, socle, Hall	C₃×C₂₉×C₇₁ ⋊ C₂
derived, Hall	C₃×C₂₉ ⋊ C₂×C₇₁
Hall	C₂₉×C₇₁ ⋊ D₃
Hall	C₃×C₇₁ ⋊ D₂₉
Sylow	C₂₉ ⋊ D₃×C₇₁
Sylow	C₃ ⋊ D₂₉×C₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇₁	D₈₇
commutator, cosocle, hypocenter	C₃×C₂₉	C₂×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₇₁	C₂
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₇₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 6177

A minimal faithful permutation representation — 2 generators on 103 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)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(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)(30,31,32)

Conjugacy classes & character table

3195 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇₁×D₈₇, D₃×D₂₉×C₇₁, D₈₇⋊D₇₁, …
maximal normal subgroup of	D₇₁×D₈₇, D₃×D₂₉×C₇₁, D₈₇⋊D₇₁, …
maximal quotient of	C₇₁×Dic₈₇, C₂×C₇₁×D₈₇, C₇₁×D₂₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12354, 7);

C71×D87 #27136403