C₁₇×#2483 #14525489

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

Aliases

direct product

C₁₇×#2483

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

700 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16932249, #16932259, #16937283, …
maximal subgroup of	C₁₇×#9500, C₁₇×#9502, C₁₇×#10338, …
maximal normal subgroup of	C₁₇×#9500, C₁₇×#9502, C₁₇×#10338, …
maximal quotient of	C₁₇×#13869, C₁₇×#13992, C₁₇×#14040, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1215);