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C₄×Dic₁₇ #63224

order	272
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

C₄×Dic₁₇

Splittings

C₁₇ ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	D₁₇
commutator, hypocenter	C₁₇	C₄²
Frattini	C₂²	C₂×D₁₇
Fitting	C₂×C₄×C₁₇	C₂
socle, prime radical, cosocle	C₂²×C₁₇	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₄

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 2 generators on 25 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(22,23,24,25);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,20,21)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₈×Dic₁₇, #10587485, #10587486, …
maximal normal subgroup of	C₈×Dic₁₇, #10587485, #10587486, …
maximal quotient of	C₄×#3622, #10587474, C₈×Dic₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 11);