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C₄×D₃₆ #63435

order	288
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₄×D₃₆

Splittings

Fitting	C₄²×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₄×D₄

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×D₉
commutator	C₂×C₉	C₂²×C₄
Frattini, socle	C₂²×C₃	C₂²×D₃
Fitting	C₄²×C₉	C₂
prime radical	C₂×D₃₆	C₂
cosocle	C₂²×C₉	C₂³
hypercenter	C₄²	D₉
hypocenter	C₉	C₄×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

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:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10588136, #10588162, C₈×D₃₆, …
maximal normal subgroup of	#10588136, #10588162, C₈×D₃₆, …
maximal quotient of	#10588333, #10588345, #10588348, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 83);