C₁₇×#2644 #14525650

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2644

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

420 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 1088

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)(19,22)(23,24)(26,27)(28,31)(29,32)(30,33)(34,35,38,40)(36,41,37,39);(18,19,21,22)(20,23,25,24)(26,28)(27,29)(30,32)(31,33)(34,36,38,37)(35,39,40,41);(18,19)(20,24)(21,22)(23,25)(26,28)(27,31)(29,33)(30,32)(34,35)(36,39)(37,41)(38,40);(18,20,21,25)(19,23,22,24)(26,29,30,31)(27,32,33,28)(34,37,38,36)(35,39,40,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17137465, #17137480, #17137555, …
maximal subgroup of	C₁₇×#29436, C₁₇×#29437, C₁₇×#29442, …
maximal normal subgroup of	C₁₇×#29436, C₁₇×#29437, C₁₇×#29442, …
maximal quotient of	C₁₇×#14260, C₁₇×#14266, C₁₇×#14331, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1376);