C₂×C₃×#19150285 #45692579

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

Aliases

direct product

C₂×C₃×#19150285

Splittings

Fitting, socle	C₂×C₃×C₇²×C₁₉ ⋊ C₂×C₃
derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₃²
Hall	C₃×#14584116 ⋊ C₂²
Hall	C₂×C₇⋊D₁₃₃ ⋊ C₃²
Sylow	C₇² ⋊ C₂×C₃×D₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×C₃×#64424

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	#19150285
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 5586

A minimal faithful permutation representation — 3 generators on 38 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1377);

C2×C3×#19150285 #45692579