#50310345

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	C₁₉⋊#10621728 ⋊ C₃
Hall	#23751432 ⋊ C₄
Sylow	C₁₃² ⋊ (C₁₉⋊C₃)⋊C₄
Sylow	C₁₉ ⋊ #14523144

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₁₉	C₃×C₄
prime radical	#34064206	C₂
cosocle	C₁₉×C₁₃⋊D₁₃	C₂×C₃
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 3211

A minimal faithful permutation representation — 3 generators on 45 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

284 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 227);