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C₂²×C₂₅×C₁₀₇ #24924135

order	10700
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 12720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₂₅×C₁₀₇
multiplicative	(ℤ/16053)ˣ, (ℤ/21404)ˣ, (ℤ/32106)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅×C₁₀₇
socle, prime radical	C₂²×C₅×C₁₀₇	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10700 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	A₄×C₂₅×C₁₀₇
maximal subgroup of	C₂²×C₃×C₂₅×C₁₀₇, A₄×C₂₅×C₁₀₇, C₂×D₃×C₂₅×C₁₀₇, …
maximal normal subgroup of	C₂²×C₃×C₂₅×C₁₀₇, A₄×C₂₅×C₁₀₇, C₂×C₄×C₂₅×C₁₀₇, …
maximal quotient of	C₂²×C₃×C₂₅×C₁₀₇, C₂×D₃×C₂₅×C₁₀₇, C₂×C₄×C₂₅×C₁₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10700, 5);