C₁₇×#2820 #14525826

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#2820

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

464 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 184 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)(22,23,25,27)(24,26,28,29)(31,34)(35,36);(19,21)(24,28)(26,29)(30,31,33,34)(32,35,37,36);(18,19)(20,21)(22,23)(24,26)(25,27)(28,29)(30,31)(32,36)(33,34)(35,37);(22,24)(23,26)(25,28)(27,29)(30,32,33,37)(31,35,34,36)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16935609, #16935628, #16935635, …
maximal subgroup of	C₁₇×#10079, C₁₇×#10082, C₁₇×#10083, …
maximal normal subgroup of	C₁₇×#10079, C₁₇×#10082, C₁₇×#10083, …
maximal quotient of	C₁₇×#14624, C₁₇×#14626, C₁₇×#14628, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1552);