C₃×C₁₃⋊D₂₄₇ #34064261

order	19266
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₃

Aliases

direct product

C₃×C₁₃⋊D₂₄₇

Splittings

Fitting, socle, Hall	C₃×C₁₃²×C₁₉ ⋊ C₂
derived, Hall	C₁₃²×C₁₉ ⋊ C₂×C₃
Hall	C₃×C₁₃² ⋊ D₁₉
Sylow	C₁₃² ⋊ C₃×D₁₉
Hall	C₃×C₁₉ ⋊ C₁₃⋊D₁₃
Sylow	C₁₉ ⋊ C₃×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊D₂₄₇
commutator, cosocle, hypocenter	C₁₃²×C₁₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₁₉	C₂
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁ ◁ C₃

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 9633

A minimal faithful permutation representation — 3 generators on 48 points:

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

Conjugacy classes & character table

4821 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₁₃×D₂₄₇, C₃×D₁₉×C₁₃⋊D₁₃, D₃₉⋊D₂₄₇, …
maximal normal subgroup of	C₃×D₁₃×D₂₄₇, C₃×D₁₉×C₁₃⋊D₁₃, D₃₉⋊D₂₄₇, …
maximal quotient of	C₃×C₁₉⋊#10621725, C₂×C₃×C₁₃⋊D₂₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19266, 96);

C3×C13⋊D247 #34064261