Finite Group Databasebeta

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C₂₅×C₃₇₃ #22605359

order	9325
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₃×C₄²×C₅×C₃₁ (order 7440) · Inn(G) = C₁ · Out(G) = C₃×C₄²×C₅×C₃₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₃₂₅
abelian	C₂₅×C₃₇₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₅	C₅×C₃₇₃
socle	C₅×C₃₇₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9325 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₉₃₂₅, Dic₉₃₂₅, #49152328, …
Fitting subgroup of	D₂₅×C₃₇₃, C₂₅×D₃₇₃, D₉₃₂₅, …
maximal subgroup of	C₂×C₂₅×C₃₇₃, D₂₅×C₃₇₃, C₂₅×D₃₇₃, …
maximal normal subgroup of	C₂×C₂₅×C₃₇₃, D₂₅×C₃₇₃, C₂₅×D₃₇₃, …
maximal quotient of	C₂×C₂₅×C₃₇₃, C₃×C₂₅×C₃₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9325, 1);