C₁₇×#2724 #14525730

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2724

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

504 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 504 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) = 37
transitive degree	μ_t(G) = 1088

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16923033, #16923116, #16923236, …
maximal subgroup of	C₁₇×#7736, C₁₇×#7751, C₁₇×#7770, …
maximal normal subgroup of	C₁₇×#7736, C₁₇×#7751, C₁₇×#7770, …
maximal quotient of	C₁₇×#14384, C₁₇×#14440, C₁₇×#14446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1456);