#50310212

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

Aliases

No aliases for this group.

Splittings

derived, Hall	C₁₃²×C₁₉ ⋊ C₃×C₄
Hall	C₁₉×#10621725 ⋊ C₃
Hall	#23751431 ⋊ C₄
Hall	#10621725 ⋊ C₁₉⋊C₃
Sylow	C₁₃² ⋊ C₄×C₁₉⋊C₃
Sylow	C₁₉ ⋊ #14523128

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#34064207
commutator, hypocenter	C₁₃²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₃²×C₁₉	C₂×C₃
prime radical	C₂×#23751431	C₂
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁ ◁ C₂

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 12844

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4)(6,10,11,7,8,12)(9,16,15,13,14,17)(19,23,24,20,21,25)(22,29,28,26,27,30)(32,33,35)(34,37,41)(36,39,38)(40,44,45)(42,46,43)(47,49,48);(18,19,22,21,25,28,27,29,30,24,23,26,20)(31,32,34,37,42,47,46,35,38,43,44,33,36,40,41,45,48,49,39);(5,6,9,8,12,15,14,16,17,11,10,13,7)

Polycyclic presentation:

2,3,13^2,19,2|a^2=f,c^a=c^12,d^a=d^12,c^b=c^3,d^b=d^3,e^b=e^11

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 94);