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#108×C₃₇₉ #27131200

order	12128
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₇₉ · Schur multiplier (H₂) = C₁

Aliases

#108×C₃₇₉

Subgroups

	subgroup	G/H
center	C₄×C₃₇₉	D₄
commutator	C₄	C₂×C₄×C₃₇₉
Frattini, cosocle	C₂×C₄	C₂²×C₃₇₉
socle	C₂×C₃₇₉	C₄⋊C₄
prime radical	C₂²×C₃₇₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇₉ ◁ C₂×C₄×C₃₇₉ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5306 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37565050, #37565056, #37565059, …
maximal subgroup of	#359×C₃₇₉, #361×C₃₇₉, #362×C₃₇₉, …
maximal normal subgroup of	#359×C₃₇₉, #361×C₃₇₉, #362×C₃₇₉, …
maximal quotient of	#334×C₃₇₉, #335×C₃₇₉, #341×C₃₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12128, 15);