C₁₇×#2211 #14525217

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2211

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₂×D₈×C₁₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

158 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,32)(25,28)(26,38)(27,41)(29,34)(30,40)(31,37)(33,48)(35,52)(36,49)(39,47)(42,46)(43,50)(44,51)(45,53);(18,19,20,21)(23,28)(29,43)(30,44)(31,41)(32,48)(38,49)(45,47)(46,52);(22,24,25,33)(23,29,28,43)(26,39,36,53)(27,42,37,35)(30,46,44,52)(31,47,41,45)(32,49,48,38)(34,51,50,40)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2211, #17188590, #17188606, …
maximal subgroup of	C₂×C₁₇×#2211, C₁₇×#33579, C₁₇×#33581, …
maximal normal subgroup of	C₂×C₁₇×#2211, C₁₇×#33579, C₁₇×#33581, …
maximal quotient of	C₁₇×#12419, C₁₇×#12423, C₁₇×#12429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 943);