#29508990

order	15450
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₅

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₅²×C₁₀₃ ⋊ C₂×C₃
Hall	C₅²⋊C₃×C₁₀₃ ⋊ C₂
Hall	C₅⋊D₅₁₅ ⋊ C₃
Sylow	C₁₀₃ ⋊ (C₅⋊D₅)⋊C₃
Hall	C₅²⋊C₃ ⋊ D₁₀₃
Sylow	C₅² ⋊ C₃×D₁₀₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₀₃	C₂×C₃
LCS	G ▷ C₅²×C₁₀₃
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 118
transitive degree	μ_t(G) = 1545

A minimal faithful permutation representation — 2 generators on 118 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)(104,105,107)(106,116,112,109,110,118)(108,113,117,114,115,111);(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)(104,106,111,117,109)(105,108,110,116,114)(107,112,113,115,118)

Polycyclic presentation:

2,3,5^2,103|c^a=c^4,d^a=d^4,e^a=e^102,c^b=cd,d^b=c^2d^3

Conjugacy classes & character table

571 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₅⋊D₅)⋊C₃×D₁₀₃, #3874⋊D₁₀₃, C₂×#29508990
maximal normal subgroup of	(C₅⋊D₅)⋊C₃×D₁₀₃, #3874⋊D₁₀₃, C₂×#29508990
maximal quotient of	#44525446, C₂×#29508990

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15450, 24);