Finite Group Databasebeta

← Prev (#26045653) Next (#26045655) →

#101×C₃₇₃ #26045654

order	11936
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₇₃ · Schur multiplier (H₂) = C₂

Aliases

#101×C₃₇₃

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇₃	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₃₇₃
Frattini, cosocle	C₂×C₄	C₂²×C₃₇₃
prime radical	C₂²×C₃₇₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇₃ ◁ C₂×C₄×C₃₇₃ ◁ G

38 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4103 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37559218, #37559220, #101×D₃₇₃, …
maximal subgroup of	#355×C₃₇₃, #356×C₃₇₃, C₂×#101×C₃₇₃, …
maximal normal subgroup of	#355×C₃₇₃, #356×C₃₇₃, C₂×#101×C₃₇₃, …
maximal quotient of	#324×C₃₇₃, #330×C₃₇₃, #332×C₃₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 8);