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C₂²×C₄₇×C₄₉ #22604241

order	9212
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11592
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₄₇×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₇	C₂²×C₇×C₄₇
socle	C₂²×C₇×C₄₇	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9212 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂²×C₄₇×C₄₉⋊C₃, A₄×C₄₇×C₄₉, C₄₇×C₂²⋊(C₄₉⋊C₃)
maximal subgroup of	C₂²×C₃×C₄₇×C₄₉, C₂²×C₄₇×C₄₉⋊C₃, A₄×C₄₇×C₄₉, …
maximal normal subgroup of	C₂²×C₃×C₄₇×C₄₉, C₂²×C₄₇×C₄₉⋊C₃, A₄×C₄₇×C₄₉, …
maximal quotient of	C₂²×C₃×C₄₇×C₄₉, C₂×D₃×C₄₇×C₄₉, C₂×C₄×C₄₇×C₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9212, 5);