C₁₃×#19056 #15705395

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₃×#19056

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3549	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 45
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 45 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 12044);