C₂×#30660727 #45692103

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

Aliases

direct product

C₂×#30660727

Splittings

Fitting, socle	C₂×C₇²×C₁₉ ⋊ C₃×D₃
derived	C₁₉×#3862 ⋊ C₂²×C₃
Hall	#22552727 ⋊ C₂²
Hall	C₇²×C₁₉ ⋊ C₂×C₃×D₃
Sylow	C₇² ⋊ C₂×D₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×#64418⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#30660727
commutator, cosocle, hypocenter	C₁₉×#3862	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₉	C₃×D₃
LCS	G ▷ C₁₉×#3862
UCS	C₁ ◁ C₂

152 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 25 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) = 532

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 901);