C₇×C₁₃×D₁₅₃ #42123797

order	27846
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₃×D₁₅₃
unambiguous semidirect product	C₉⋊(C₇×C₁₃×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₇×C₁₃×D₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₁₅₃
commutator, cosocle, hypocenter	C₉×C₁₇	C₂×C₇×C₁₃
Frattini	C₃	C₇×C₁₃×D₅₁
Fitting	C₇×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₇×C₁₃×C₁₇	D₃
LCS	G ▷ C₉×C₁₇
UCS	C₁ ◁ C₇×C₁₃

48 conjugacy classes of subgroups.

μ_t(G) = 13923

7098 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27846, 14);