C₂×C₄₇×D₇₁ #27211155

order	13348
isoclinism	isoclinic class of D₇₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₄₇×D₇₁
unambiguous semidirect product	C₇₁⋊(C₂²×C₄₇)
unambiguous semidirect product	(C₂×C₇₁)⋊(C₂×C₄₇)

Splittings

Fitting, socle	C₂×C₄₇×C₇₁ ⋊ C₂
derived, Sylow	C₇₁ ⋊ C₂²×C₄₇
Hall	C₄₇×C₇₁ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₇₁
commutator, cosocle, hypocenter	C₇₁	C₂²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₇₁	C₂
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₄₇

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 120
transitive degree	μ_t(G) = 6674

A minimal faithful permutation representation — 2 generators on 120 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)(68,69)(70,71)(72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(119,120)

Conjugacy classes & character table

3478 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13348, 9);

C2×C47×D71 #27211155