Finite Group Databasebeta

← Prev (#38738367) Next (#38738369) →

#1434×C₁₉₇ #38738368

order	25216
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

#1434×C₁₉₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉₇	C₂³
commutator	C₂²	C₂×C₄²×C₁₉₇
Frattini, cosocle	C₂⁴	C₂³×C₁₉₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉₇ ◁ G

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 25216

Conjugacy classes & character table

11032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 166);