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C₃×#87641 #11924228

order	1176
isoclinism	isoclinic class of #87640
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Hall	C₃×C₇² ⋊ D₄
Sylow	C₇² ⋊ C₃×D₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₇²
commutator, cosocle	C₂×C₇²	C₂²×C₃
Frattini	C₂	C₃×D₇²
Fitting, socle	C₂×C₃×C₇²	C₂²
hypocenter	C₇²	C₃×D₄
LCS	G ▷ C₂×C₇² ▷ C₇²
UCS	C₁ ◁ C₂×C₃

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 84

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#11924176, C₃×#11716115, D₃×#87641, …
maximal normal subgroup of	C₃×#11924176, C₃×#11716115, D₃×#87641, …
maximal quotient of	C₃×#11924253, C₂×C₃×#87641, C₃×#11716036, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 143);