C₁₇×#2622 #14525628

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#2622

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#120	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

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

normal subgroups only

This group has 702 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) = 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)(22,23)(24,27)(25,26)(28,29)(31,34)(35,36);(19,21)(23,26)(27,28)(30,31,33,34)(32,35,37,36);(18,19)(20,21)(22,23)(24,28)(25,26)(27,29)(30,31)(32,36)(33,34)(35,37);(22,24)(23,27)(25,29)(26,28)(30,32)(31,35)(33,37)(34,36)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17067572, #17068196, D₁₇×#2622, …
maximal subgroup of	C₁₇×#24058, C₁₇×#24114, C₂×C₁₇×#2622, …
maximal normal subgroup of	C₁₇×#24058, C₁₇×#24114, C₂×C₁₇×#2622, …
maximal quotient of	C₁₇×#14255, C₁₇×#14259, C₁₇×#14262, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1354);