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C₂²×C₄²×C₁₉₃ #27134902

order	12352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 28311552
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄²×C₁₉₃
multiplicative	(ℤ/30920)ˣ, (ℤ/37104)ˣ, (ℤ/46380)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₁₉₃
socle, prime radical	C₂⁴×C₁₉₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×#95×C₁₉₃, #1434×C₁₉₃, C₄⋊#95×C₁₉₃, …
maximal normal subgroup of	C₄×#95×C₁₉₃, #1434×C₁₉₃, C₄⋊#95×C₁₉₃, …
maximal quotient of	C₂×C₄³×C₁₉₃, C₂²×#95×C₁₉₃, C₂×#376×C₁₉₃, …
automorphism group of	C₅×C₈×C₇₇₃
outer automorphism group of	C₅×C₈×C₇₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 192);