C₁₇×#2634 #14525640

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

Aliases

direct product

C₁₇×#2634

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 192 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 192 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)(23,26)(27,29)(30,31,35,33)(32,38,40,36)(34,37,42,41)(39,44,45,43);(19,21)(23,26)(27,29)(30,32,35,40)(31,36,33,38)(34,39,42,45)(37,43,41,44);(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,33,35,31)(32,36,40,38)(34,37,42,41)(39,44,45,43);(22,24,25,28)(23,27,26,29)(30,34)(31,37)(32,39)(33,41)(35,42)(36,43)(38,44)(40,45)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16930323, #16935221, #16935249, …
maximal subgroup of	C₁₇×#9190, C₁₇×#10021, C₁₇×#10025, …
maximal normal subgroup of	C₁₇×#9190, C₁₇×#10021, C₁₇×#10025, …
maximal quotient of	C₁₇×#14270, C₁₇×#14289, C₁₇×#14298, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1366);