C₁₇×#2401 #14525407

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2401

Subgroups

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

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

normal subgroups only

This group has 432 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)(18,19)(20,23)(21,22)(24,25)(26,27,29,31)(28,30,32,33)(34,35,37,39)(36,38,40,41);(19,22)(23,25)(26,28,29,32)(27,30,31,33)(34,36)(35,38)(37,40)(39,41);(27,31)(30,33)(36,40)(38,41);(18,20,21,24)(19,23,22,25)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17042582, #17042593, #17042604, …
maximal subgroup of	C₁₇×#21668, C₁₇×#21669, C₁₇×#21670, …
maximal normal subgroup of	C₁₇×#21668, C₁₇×#21669, C₁₇×#21670, …
maximal quotient of	C₁₇×#13842, C₁₇×#13846, C₁₇×#13855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1133);