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C₂²×C₉×C₂₉₃ #24902125

order	10548
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10512
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₉×C₂₉₃
multiplicative	(ℤ/11153)ˣ, (ℤ/15849)ˣ, (ℤ/22306)ˣ, (ℤ/31698)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₂₉₃
socle, prime radical	C₂²×C₃×C₂₉₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 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×C₄×C₉×C₂₉₃, C₂³×C₉×C₂₉₃, C₂²×C₂₇×C₂₉₃, …
maximal normal subgroup of	C₂×C₄×C₉×C₂₉₃, C₂³×C₉×C₂₉₃, C₂²×C₂₇×C₂₉₃, …
maximal quotient of	C₂×C₄×C₉×C₂₉₃, C₂³×C₉×C₂₉₃, C₂²×C₂₇×C₂₉₃, …
automorphism group of	C₁₉×C₅₈₇, C₂×C₂₇×C₅₈₇
outer automorphism group of	C₁₉×C₅₈₇, C₂×C₂₇×C₅₈₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10548, 5);