#43245144

order	28158
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₃×C₁₉² ⋊ C₂×C₃
Hall	#28381095 ⋊ C₂
Hall	C₁₃⋊(C₁₉⋊D₁₉) ⋊ C₃
Sylow	C₁₉² ⋊ D₁₃⋊C₃
Sylow	C₁₃ ⋊ #14524206

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₉²	C₂×C₃
LCS	G ▷ C₁₃×C₁₉²
UCS	C₁

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 4693

A minimal faithful permutation representation — 3 generators on 51 points:

(2,6,7,3,4,8)(5,12,11,9,10,13)(15,19,20,16,17,21)(18,27,24,22,23,29)(25,30,32,31,28,26)(34,38,39,35,36,40)(37,46,43,41,42,48)(44,49,51,50,47,45);(1,2,5,4,8,11,10,12,13,7,6,9,3)(33,34,37,43,49,46,50,36,40,45,51,39,38,44,42,47,48,41,35);(14,15,18,24,30,27,31,17,21,26,32,20,19,25,23,28,29,22,16)

Polycyclic presentation:

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

Conjugacy classes & character table

788 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28158, 45);