C₁₇×#2369 #14525375

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#2369

Subgroups

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

496 conjugacy classes of subgroups; only the 328 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 328 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 — 4 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23,26,25)(24,28,29,27)(31,34)(35,36);(18,20,21,19)(23,25)(27,28)(30,31)(32,36)(33,34)(35,37);(22,24,26,29)(23,27,25,28);(22,25,26,23)(24,28,29,27)(30,32,33,37)(31,35,34,36)

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16928783, #16928789, #16928794, …
maximal subgroup of	C₁₇×#8927, C₁₇×#8928, C₁₇×#8929, …
maximal normal subgroup of	C₁₇×#8927, C₁₇×#8928, C₁₇×#8929, …
maximal quotient of	C₄⋊C₄²×C₁₇, C₁₇×#13818, C₁₇×#13826, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1101);