C₂×C₂₉×#382 #16815995

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×C₂₉×#382

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	C₂³
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

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

normal subgroups only

This group has 712 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) = 47
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(4,5)(7,8,9,10)(13,17)(15,18);(3,4,6,5)(11,12,14,16)(13,15,17,18);(3,5,6,4)(11,13)(12,15)(14,17)(16,18)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7914, C₂×C₂₉×#1286, C₂₉×#7959, …
maximal normal subgroup of	C₂₉×#7914, C₂×C₂₉×#1286, C₂₉×#7959, …
maximal quotient of	C₂×C₂₉×#1434, C₂×C₂₉×C₄⋊#95, C₄×C₂₉×#382, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1013);