C₃×#26013885 #45692232

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product

C₃×#26013885

Splittings

Fitting, socle	C₃×C₇²×C₁₉ ⋊ C₂²×C₃
derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₃²
Hall	C₃×#14584116 ⋊ C₂²
Hall	D₁₉×C₇⋊D₇ ⋊ C₃²
Sylow	C₇² ⋊ C₂×C₃×D₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×C₃×#64424

Subgroups

	subgroup	G/H
center, hypercenter	C₃	#26013885
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂²×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₃

600 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 36
transitive degree	μ_t(G) = 2793

A minimal faithful permutation representation — 3 generators on 36 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1030);