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C₂²×C₄₉×C₅₃ #23780726

order	10388
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 13104
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₄₉×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₂²×C₇×C₅₃
socle, prime radical	C₂²×C₇×C₅₃	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10388 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂²×C₅₃×C₄₉⋊C₃, A₄×C₄₉×C₅₃, C₅₃×C₂²⋊(C₄₉⋊C₃)
maximal subgroup of	C₂²×C₃×C₄₉×C₅₃, C₂²×C₅₃×C₄₉⋊C₃, A₄×C₄₉×C₅₃, …
maximal normal subgroup of	C₂²×C₃×C₄₉×C₅₃, C₂²×C₅₃×C₄₉⋊C₃, A₄×C₄₉×C₅₃, …
maximal quotient of	C₂²×C₃×C₄₉×C₅₃, C₂×D₃×C₄₉×C₅₃, C₂×C₄×C₄₉×C₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10388, 5);