C₁₇×#2141 #14525147

order	2176
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2141

Subgroups

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

220 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 104 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)(18,19,20,21)(22,23)(24,33)(25,30)(26,39)(27,43)(28,32)(29,35)(31,41)(34,47)(36,53)(37,50)(38,48)(40,46)(42,49)(44,51)(45,52);(22,24,28,37)(23,29,32,45)(25,36,27,34)(26,40,42,51)(30,46,43,44)(31,47,48,53)(33,49,50,39)(35,38,52,41);(22,25,28,27)(23,30,32,43)(24,34,37,36)(26,38,42,41)(29,44,45,46)(31,39,48,49)(33,47,50,53)(35,51,52,40)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16949604, #16950013, #16950068, …
maximal subgroup of	C₁₇×#12648, C₁₇×#12742, C₁₇×#12751, …
maximal normal subgroup of	C₁₇×#12648, C₁₇×#12742, C₁₇×#12751, …
maximal quotient of	C₁₇×#11594, C₁₇×#11650, C₁₇×#11662, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 873);