C₂×C₁₇×#381 #14525285

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂×C₁₇×#381

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂³
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

1144 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 440 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) = 35
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16923936, C₂×#14526636, #16924051, …
maximal subgroup of	C₁₇×#7913, C₂×C₁₇×#1284, C₁₇×#7943, …
maximal normal subgroup of	C₁₇×#7913, C₂×C₁₇×#1284, C₁₇×#7943, …
maximal quotient of	C₂×C₁₇×C₂²⋊#95, C₂×C₁₇×#1434, C₄×C₁₇×#381, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1011);