#34038115

order	18849
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₆₁×C₁₀₃ ⋊ C₃
Sylow	C₁₀₃ ⋊ C₆₁⋊C₃
Sylow	C₆₁ ⋊ C₁₀₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₆₁×C₁₀₃	C₃
LCS	G ▷ C₆₁×C₁₀₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 164
transitive degree	μ_t(G) = 6283

A minimal faithful permutation representation — 2 generators on 164 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,69)(41,56,66)(44,59,64)(47,62,61)(50,54,58)(52,67,55)(57,72,84)(60,75,82)(63,78,80)(65,73,77)(68,83,74)(70,85,71)(76,88,95)(79,90,94)(81,89,92)(86,96,87)(91,97,101)(93,98,100)(99,102,103)(105,106,108)(107,110,115)(109,113,112)(111,117,125)(114,120,122)(116,123,119)(118,127,137)(121,129,134)(124,132,131)(126,135,128)(130,140,147)(133,142,144)(136,145,141)(138,148,139)(143,151,155)(146,153,152)(149,156,150)(154,159,160)(157,161,158)(162,164,163);(1,2,4,8,15,25,38,54,33,12,19,29,42,58,74,87,96,67,35,48,64,80,92,72,37,52,68,69,84,95,101,103,97,75,40,14,23,34,47,63,79,91,98,78,43,17,3,6,11,18,28,41,57,73,46,20,5,9,16,26,39,55,71,83,49,22,32,45,61,77,53,70,86,85,51,66,82,94,100,88,56,24,36,50,65,81,93,99,102,90,59,27,7,13,21,31,44,60,76,89,62,30,10)(104,105,107,111,118,127,138,149,157,162,161,145,123,108,112,119,128,139,140,117,126,136,146,154,156,135,115,122,131,141,150,151,129,110,116,124,133,143,148,125,134,144,152,158,159,142,120,106,109,114,121,130,137,147,155,160,163,164,153,132,113)

Polycyclic presentation:

3,61,103|b^a=b^47,c^a=c^46

Conjugacy classes & character table

2097 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#34038115, #49179339, #49179343, …
maximal normal subgroup of	C₂×#34038115, #49179339, #49179343, …
maximal quotient of	C₂×#34038115

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18849, 4);