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C₂²×C₃²×C₂₉₃ #24902139

order	10548
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 84096
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃²×C₂₉₃
multiplicative	(ℤ/12313)ˣ, (ℤ/15831)ˣ, (ℤ/24626)ˣ, (ℤ/31662)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10548 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₂₉₃, C₂³×C₃²×C₂₉₃, C₂²×C₃×C₉×C₂₉₃, …
maximal normal subgroup of	C₂×C₃²×C₄×C₂₉₃, C₂³×C₃²×C₂₉₃, C₂²×C₃×C₉×C₂₉₃, …
maximal quotient of	C₂×C₃²×C₄×C₂₉₃, C₂³×C₃²×C₂₉₃, C₂²×C₃×C₉×C₂₉₃, …
automorphism group of	C₇×C₁₇₅₉
outer automorphism group of	C₇×C₁₇₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10548, 19);