C₁₉⋊C₃×#10596868 #45691815

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉⋊C₃×#10596868

Splittings

derived	C₁₉×#3862 ⋊ C₃×C₄
Hall	C₁₉⋊C₃×#3862 ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃×Dic₃
Sylow	C₇² ⋊ Dic₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₃×#10596868

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₉⋊C₃×#64418
commutator, hypocenter	C₁₉×#3862	C₃×C₄
Fitting, socle	C₂×C₇²×C₁₉	C₃×D₃
prime radical	C₂×C₁₉⋊C₃×#3862	C₂
cosocle	C₂×C₁₉×#3862	C₂×C₃
LCS	G ▷ C₁₉×#3862
UCS	C₁ ◁ C₂

104 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 21 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) = 532

A minimal faithful permutation representation — 2 generators on 37 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 613);