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C₂²×C₂₅×C₇₉ #21463583

order	7900
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₂₅×C₇₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₅	C₂²×C₅×C₇₉
socle	C₂²×C₅×C₇₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7900 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂²×C₂₅×C₇₉⋊C₃, A₄×C₂₅×C₇₉, C₂₅×C₂²⋊(C₇₉⋊C₃)
maximal subgroup of	C₂²×C₃×C₂₅×C₇₉, C₂²×C₂₅×C₇₉⋊C₃, A₄×C₂₅×C₇₉, …
maximal normal subgroup of	C₂²×C₃×C₂₅×C₇₉, C₂²×C₂₅×C₇₉⋊C₃, A₄×C₂₅×C₇₉, …
maximal quotient of	C₂²×C₃×C₂₅×C₇₉, C₂×D₃×C₂₅×C₇₉, C₂×C₄×C₂₅×C₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7900, 5);