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D₄×Dic₉ #63496

order	288
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

D₄×Dic₉

Splittings

C₉ ⋊ C₄×D₄

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₉
commutator	C₂×C₉	C₂²×C₄
Frattini, socle	C₂²×C₃	C₂²×D₃
Fitting	C₂×D₄×C₉	C₂
prime radical	C₂×C₃×D₄	D₃
cosocle	C₂²×C₉	C₂³
hypercenter	C₂×D₄	D₉
hypocenter	C₉	C₄×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×D₄

141 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

(2,4)(3,7)(5,6)(8,9)(10,11,12,13);(1,6,8,7,2,4,3,9,5)(15,17);(14,15)(16,17)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10588436, #10588437, #10588438, …
maximal normal subgroup of	#10588436, #10588437, #10588438, …
maximal quotient of	C₂²⋊C₄×Dic₉, #10588630, #10588631, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 144);