C₁₇×#2642 #14525648

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#2642

Subgroups

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

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

normal subgroups only

This group has 416 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) = 45
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(24,28)(26,29)(31,35)(36,38)(37,43)(44,45);(18,19,20,21)(22,23,25,27)(24,26,28,29)(30,31)(32,38)(33,37)(34,35)(36,40)(39,45)(41,44)(42,43);(18,19)(20,21)(22,24)(23,26)(25,28)(27,29)(30,32,34,40)(31,36,35,38)(33,41,42,39)(37,45,43,44);(30,33,34,42)(31,37,35,43)(32,39,40,41)(36,44,38,45)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16935715, #16935771, #17009547, …
maximal subgroup of	C₁₇×#10095, C₁₇×#10103, C₁₇×#18441, …
maximal normal subgroup of	C₁₇×#10095, C₁₇×#10103, C₁₇×#18441, …
maximal quotient of	C₁₇×#14261, C₁₇×#14274, C₁₇×#14283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1374);