#50310360

order	38532
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₃²×C₁₉ ⋊ C₃×C₄
Hall	C₁₃×C₁₉⋊#261 ⋊ C₃
Hall	#23751432 ⋊ C₄
Sylow	C₁₃² ⋊ (C₁₉⋊C₃)⋊C₄
Sylow	C₁₉ ⋊ #14523152

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₁₉	C₃×C₄
prime radical	#34064216	C₂
cosocle	C₁₃×C₁₉×D₁₃	C₂×C₃
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 988

A minimal faithful permutation representation — 2 generators on 45 points:

(2,6,11,7,4,8,5,12,9,3,10,13)(15,16,18)(17,20,23)(19,22,21)(24,26,25)(28,32,33,29,30,34)(31,40,37,35,36,42)(38,43,45,44,41,39);(1,2,6,4,11,3,8,13,7,9,10,12,5)(14,15,17,16,19,23,20,24,26,18,21,25,22)(27,28,31,37,43,40,44,30,34,39,45,33,32,38,36,41,42,35,29)

Polycyclic presentation:

2,3,2,13^2,19|a^2=c,d^a=d^5,f^a=f^18,d^b=d^3,e^b=e^3,f^b=f^7,d^c=d^12

Conjugacy classes & character table

353 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 242);