C₃×D₁₃⋊C₁₆ #11928334

order	1248
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×D₁₃⋊C₁₆

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₃×C₁₆
Hall	C₃×C₁₃ ⋊ C₂×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₈	#261
commutator, hypocenter	C₁₃	C₂×C₃×C₁₆
Frattini	C₄	C₂×C₃×#261
Fitting	C₃×C₈×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₂×C₈
prime radical	C₂×C₃×D₁₃	C₈
cosocle	#1055	C₂²×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₈

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 624

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 446);

C3×D13⋊C16 #11928334

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₃×D₁₃⋊C₁₆ #11928334