#34093065

order	19950
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₅

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₅²×C₇×C₁₉ ⋊ C₂×C₃
Hall	C₅²⋊#87705 ⋊ C₂
Hall	C₅⋊D₆₆₅ ⋊ C₃
Hall	C₅²×C₁₉ ⋊ AGL(1,𝔽₇)
Hall	C₅²×C₇ ⋊ D₁₉⋊C₃
Hall	C₇×C₁₉ ⋊ (C₅⋊D₅)⋊C₃
Sylow	C₅² ⋊ #11716328
Sylow	C₁₉ ⋊ #11760386
Sylow	C₇ ⋊ #15668133

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₇×C₁₉
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1995

A minimal faithful permutation representation — 2 generators on 41 points:

(2,6,7,3,4,8)(5,13,14,9,10,18)(11,19,17,16,15,12)(21,24,25,22,23,26)(27,28,30)(29,39,35,32,33,41)(31,36,40,37,38,34);(1,2,5,10,15,18,17,7,6,11,16,4,8,12,14,19,13,9,3)(20,21,23,26,25,24,22)(27,29,34,40,32)(28,31,33,39,37)(30,35,36,38,41)

Polycyclic presentation:

2,3,5^2,7,19|c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^18,c^b=cd,d^b=c^2d^3,e^b=e^2,f^b=f^11

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 104);