Finite Group Databasebeta

← Prev (#14524341) Next (#14524343) →

C₁₇×#1336 #14524342

order	2176
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#102
commutator	C₈	C₂×C₈×C₁₇
Frattini, cosocle	C₄×C₈	C₂²×C₁₇
socle	C₂×C₁₇	D₄⋊C₈
prime radical	C₁₇×#135	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,27,33,32,24,28,21,30,31,20,29,25);(18,20)(19,23)(21,25)(22,32)(24,27)(26,29)(28,31)(30,33)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1336, #16944117, #16944403, …
maximal subgroup of	C₂×C₁₇×#1336, C₁₇×#11604, C₁₇×#11669, …
maximal normal subgroup of	C₂×C₁₇×#1336, C₁₇×#11604, C₁₇×#11669, …
maximal quotient of	C₁₇×#7070, C₁₇×#7071, C₁₇×#7072, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 68);