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C₉×Dic₁₄ #92598

order	504
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×Dic₁₄

Splittings

Hall	C₇×C₉ ⋊ Q₈
Sylow	C₇ ⋊ Q₈×C₉

Subgroups

	subgroup	G/H
center	C₂×C₉	C₂×D₇
commutator	C₂×C₇	C₂²×C₉
Frattini	C₂×C₃	C₂×C₃×D₇
Fitting	C₄×C₇×C₉	C₂
socle, prime radical, cosocle	C₂×C₃×C₇	C₂²×C₃
hypercenter	C₄×C₉	D₇
hypocenter	C₇	Q₈×C₉
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,4,6,7,5,3)(8,10,11,15)(9,12,13,14)(16,17,19,18,20,22,21,23,24);(2,3)(4,5)(6,7)(8,9,11,13)(10,14,15,12)

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11758866, #11758867, #11758868, …
maximal normal subgroup of	#11758866, #11758867, #11758868, …
maximal quotient of	C₉×Dic₇⋊C₄, C₉×C₄⋊Dic₇, C₂×C₉×Dic₁₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 24);