C₁₇×#3004 #14526010

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#3004

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

738 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 224 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)(18,19)(20,21)(22,23)(24,30)(25,33)(26,28)(27,31)(29,35)(32,37)(34,36);(22,24,26,32)(23,27,28,36)(25,34,35,31)(29,37,33,30);(19,21);(23,28)(27,36)(29,33)(30,37)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16932345, #17006723, #17006801, …
maximal subgroup of	C₁₇×#9519, C₁₇×#18136, C₁₇×#18146, …
maximal normal subgroup of	C₁₇×#9519, C₁₇×#18136, C₁₇×#18146, …
maximal quotient of	C₁₇×#18133, C₁₇×#18138, C₁₇×#18143, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1736);