C₁₇×#2327 #14525333

order	2176
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#2327

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

516 conjugacy classes of subgroups; only the 296 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 296 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) = 41
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,25,24)(27,31)(28,34)(29,37)(39,41);(22,24,25,23)(26,27)(28,35)(29,33)(30,31)(32,34)(36,41)(37,38)(39,40);(18,19,20,21)(26,28)(27,32)(29,36)(30,34)(31,35)(33,39)(37,40)(38,41);(26,29,30,37)(27,33,31,38)(28,36,34,40)(32,39,35,41)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16929825, #16929845, #16931030, …
maximal subgroup of	C₁₇×#9100, C₁₇×#9104, C₁₇×#9296, …
maximal normal subgroup of	C₁₇×#9100, C₁₇×#9104, C₁₇×#9296, …
maximal quotient of	C₁₇×#13779, C₁₇×#13786, C₁₇×#13790, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1059);