C₁₇×#1296 #14524302

order	2176
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1296

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂²⋊C₄
commutator	C₂×C₄	C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂²×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

188 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 2176

A minimal faithful permutation representation — 2 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)(23,27)(24,25)(28,29)(30,31)(32,34)(33,36)(35,37);(22,23,25,28,26,29,24,27)(31,34)(32,37)(35,36)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921875, #16921953, D₁₇×#1296, …
maximal subgroup of	C₁₇×#7417, C₁₇×#7443, C₂×C₁₇×#1296, …
maximal normal subgroup of	C₁₇×#7417, C₁₇×#7443, C₂×C₁₇×#1296, …
maximal quotient of	C₁₇×#7025, C₁₇×#7031, C₁₇×#7039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 28);