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C₂²×Dic₁₈ #63704

order	288
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂²×Dic₁₈

Splittings

C₉ ⋊ C₂²×Q₈

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₉
commutator, cosocle	C₂×C₉	C₂⁴
Frattini	C₂×C₃	C₂³×D₃
Fitting	C₂²×C₄×C₉	C₂
socle, prime radical	C₂³×C₃	C₂×D₃
hypercenter	C₂²×C₄	D₉
hypocenter	C₉	C₂²×Q₈
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10588326, #10588336, #10588353, …
maximal normal subgroup of	#10588326, #10588336, #10588353, …
maximal quotient of	C₂×C₄×Dic₁₈, C₂×#63431, C₂×#63432, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 352);