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#104×C₃₈₃ #27133706

order	12256
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₈₃ · Schur multiplier (H₂) = C₂

Aliases

#104×C₃₈₃

Subgroups

	subgroup	G/H
center	C₄×C₃₈₃	D₄
commutator	C₄	C₂×C₄×C₃₈₃
Frattini, cosocle	C₂×C₄	C₂²×C₃₈₃
socle	C₂×C₃₈₃	C₂²⋊C₄
prime radical	#41×C₃₈₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₈₃ ◁ C₂×C₄×C₃₈₃ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5362 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#104×D₃₈₃, #37588366, #37588465, …
maximal subgroup of	C₂×#104×C₃₈₃, #421×C₃₈₃, #443×C₃₈₃, …
maximal normal subgroup of	C₂×#104×C₃₈₃, #421×C₃₈₃, #443×C₃₈₃, …
maximal quotient of	D₄⋊C₈×C₃₈₃, Q₈⋊C₈×C₃₈₃, #327×C₃₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12256, 11);