C₂×C₁₃⋊#11925892 #44538210

order	31460
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₃⋊#11925892
unambiguous semidirect product	(C₂×C₁₃)⋊#11925892

Splittings

Fitting, socle	C₂×C₁₁²×C₁₃ ⋊ C₂×C₅
derived, Hall	C₁₁²×C₁₃ ⋊ C₂²×C₅
Hall	C₁₃×#10597243 ⋊ C₂²
Hall	C₂×C₁₁⋊D₁₄₃ ⋊ C₅
Hall	#10597243 ⋊ C₂×D₁₃
Sylow	C₁₁² ⋊ C₂×C₅×D₁₃
Sylow	C₁₃ ⋊ C₂×#11925892

Subgroups

	subgroup	G/H
center, hypercenter	C₂	C₁₃⋊#11925892
commutator, cosocle, hypocenter	C₁₁²×C₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₁₃	C₂×C₅
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁ ◁ C₂

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 3146

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 150);

C2×C13⋊#11925892 #44538210