C₁₇×#2614 #14525620

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#2614

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

782 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 232 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)(23,25)(26,27,30,33)(28,34,36,31)(29,32,38,37)(35,40,41,39);(19,21)(23,25)(26,28,30,36)(27,31,33,34)(29,35,38,41)(32,39,37,40);(18,19)(20,21)(22,23)(24,25)(26,27)(28,34)(29,37)(30,33)(31,36)(32,38)(35,39)(40,41);(26,29)(27,32)(28,35)(30,38)(31,39)(33,37)(34,40)(36,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17007493, #17007515, #17065949, …
maximal subgroup of	C₁₇×#18225, C₁₇×#18227, C₁₇×#23905, …
maximal normal subgroup of	C₁₇×#18225, C₁₇×#18227, C₁₇×#23905, …
maximal quotient of	C₁₇×#14256, C₁₇×#14263, C₁₇×#14301, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1346);