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C₃×#88100 #11928337

order	1248
isoclinism	isoclinic class of #6118
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂

Aliases

Splittings

Fitting	C₃×C₈×C₁₃ ⋊ C₄
Hall	C₃×C₁₃ ⋊ #97
Sylow	C₁₃ ⋊ C₃×#97

Subgroups

	subgroup	G/H
center	C₃×C₄	C₂×#261
commutator	C₂×C₁₃	C₃×C₄²
Frattini	C₄	C₂×C₃×#261
Fitting	C₃×C₈×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₄²
prime radical	C₂×C₃×D₁₃	C₂×C₄
cosocle	C₄×D₁₃	C₂²×C₃
hypercenter	C₃×C₈	#261
hypocenter	C₁₃	C₃×#97
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃×C₄ ◁ C₃×C₈

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 312

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(4,5,8,11,15,9,13,14,6,10,16,12,7)(17,18,19,22,20,21,23,24);(5,6,7,9)(8,11,12,16)(10,14,15,13)(18,21)(22,24)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 449);