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#391×C₁₉₇ #27160602

order	12608
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

#391×C₁₉₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉₇	C₂³
commutator	C₂²	C₂²×C₄×C₁₉₇
Frattini, cosocle	C₂³	C₂³×C₁₉₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉₇ ◁ G

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12608

Conjugacy classes & character table

5516 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#38740538, #38740646, #38740839, …
maximal subgroup of	#1272×C₁₉₇, #1319×C₁₉₇, #1394×C₁₉₇, …
maximal normal subgroup of	#1272×C₁₉₇, #1319×C₁₉₇, #1394×C₁₉₇, …
maximal quotient of	C₄⋊#95×C₁₉₇, #1436×C₁₉₇, #1441×C₁₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12608, 72);