C₅×C₁₁⋊D₂₅₃ #42123742

order	27830
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₅×C₁₁⋊D₂₅₃
unambiguous semidirect product	C₂₃⋊(C₅×C₁₁⋊D₁₁)

Splittings

Fitting, socle, Hall	C₅×C₁₁²×C₂₃ ⋊ C₂
derived, Hall	C₁₁²×C₂₃ ⋊ C₂×C₅
Hall	C₅×C₁₁² ⋊ D₂₃
Sylow	C₁₁² ⋊ C₅×D₂₃
Hall	C₅×C₂₃ ⋊ C₁₁⋊D₁₁
Sylow	C₂₃ ⋊ C₅×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊D₂₅₃
commutator, cosocle, hypocenter	C₁₁²×C₂₃	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₂₃	C₂
LCS	G ▷ C₁₁²×C₂₃
UCS	C₁ ◁ C₅

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 13915

A minimal faithful permutation representation — 3 generators on 50 points:

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

Conjugacy classes & character table

6965 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27830, 64);

C5×C11⋊D253 #42123742