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H(3,ℤ/4)×C₁₆₇ #24922738

order	10688
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₆₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

H(3,ℤ/4)×C₁₆₇

Subgroups

	subgroup	G/H
center	C₄×C₁₆₇	C₄²
commutator	C₄	C₄²×C₁₆₇
Frattini, cosocle	C₂²×C₄	C₂²×C₁₆₇
socle	C₂×C₁₆₇	#95
prime radical	C₂³×C₁₆₇	D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₆₇ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3674 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36322122, #36322125, H(3,ℤ/4)×D₁₆₇, …
maximal subgroup of	#1339×C₁₆₇, #1340×C₁₆₇, C₂×H(3,ℤ/4)×C₁₆₇, …
maximal normal subgroup of	#1339×C₁₆₇, #1340×C₁₆₇, C₂×H(3,ℤ/4)×C₁₆₇, …
maximal quotient of	#1274×C₁₆₇, #1275×C₁₆₇, #1284×C₁₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 18);