#347×D₁₀₃ #27196744

order	13184
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²

Aliases

direct product

#347×D₁₀₃

Splittings

Fitting	#347×C₁₀₃ ⋊ C₂
Sylow	C₁₀₃ ⋊ C₂×#347

Subgroups

	subgroup	G/H
center	C₄	C₄²×D₁₀₃
commutator	C₄×C₁₀₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×D₁₀₃
Fitting	#347×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×#97
prime radical	C₂²×D₁₀₃	M₁₆
cosocle	C₂×C₈×C₁₀₃	C₂³
hypercenter	#347	D₁₀₃
hypocenter	C₁₀₃	C₂×#347
LCS	G ▷ C₄×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ #347

168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 1648

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

Conjugacy classes & character table

1166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 6110);