C₁₇×#2607 #14525613

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#2607

Subgroups

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

444 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 200 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)(26,27)(28,32)(29,30)(31,33)(34,35,38,37)(36,40,41,39);(19,22)(23,25)(27,30)(31,32)(36,41)(39,40);(18,19)(20,23)(21,22)(24,25)(26,27)(28,31)(29,30)(32,33)(34,36,38,41)(35,39,37,40);(18,20,21,24)(19,23,22,25)(26,28)(27,31)(29,33)(30,32)(34,37,38,35)(36,40,41,39)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16937553, #16937558, #16946530, …
maximal subgroup of	C₁₇×#10386, C₁₇×#10387, C₁₇×#12121, …
maximal normal subgroup of	C₁₇×#10386, C₁₇×#10387, C₁₇×#12121, …
maximal quotient of	C₁₇×#13953, C₁₇×#14091, C₁₇×#14093, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1339);