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#365×C₁₆₇ #24922766

order	10688
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₆₇ · Schur multiplier (H₂) = C₁

Aliases

#365×C₁₆₇

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₆₇	#106
commutator	C₈	C₂×C₄×C₁₆₇
Frattini, cosocle	C₂×C₈	C₂²×C₁₆₇
prime radical	C₂²×C₁₆₇	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆₇ ◁ C₂×C₄×C₁₆₇ ◁ C₂×C₈×C₁₆₇ ◁ G

42 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2672 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#365×D₁₆₇, #36325909, #36326028, …
maximal subgroup of	C₂×#365×C₁₆₇, #2155×C₁₆₇, #2180×C₁₆₇, …
maximal normal subgroup of	C₂×#365×C₁₆₇, #2155×C₁₆₇, #2180×C₁₆₇, …
maximal quotient of	#1368×C₁₆₇, #1383×C₁₆₇, C₂×#365×C₁₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 46);