Finite Group Databasebeta

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#362×C₁₃₇ #22576897

order	8768
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₇ · Schur multiplier (H₂) = C₂

Aliases

#362×C₁₃₇

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃₇	#102
commutator	C₈	C₂×C₄×C₁₃₇
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₇
prime radical	C₂²×C₁₃₇	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₇ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₈×C₁₃₇ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2192 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#362×D₁₃₇, #31782537, #31782683, …
maximal subgroup of	C₂×#362×C₁₃₇, #2148×C₁₃₇, #2180×C₁₃₇, …
maximal normal subgroup of	C₂×#362×C₁₃₇, #2148×C₁₃₇, #2180×C₁₃₇, …
maximal quotient of	#1334×C₁₃₇, #1350×C₁₃₇, #1362×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 43);