#50310340

order	38532
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₃²×C₁₉ ⋊ C₂²×C₃
Hall	D₁₉×C₁₃⋊D₁₃ ⋊ C₃
Hall	#23751432 ⋊ C₂²
Sylow	C₁₃² ⋊ C₂×D₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×#11759815

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₁₉	C₂²×C₃
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁

320 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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

326 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 222);