C₂×C₁₉×C₇⋊D₆₃ #45691708

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₁₉×C₇⋊D₆₃
unambiguous semidirect product	(C₂×C₇)⋊(C₁₉×D₆₃)
unambiguous semidirect product	(C₂×C₉)⋊(C₁₉×C₇⋊D₇)

Splittings

Fitting	C₂×C₇²×C₉×C₁₉ ⋊ C₂
derived, Hall	C₇²×C₉ ⋊ C₂²×C₁₉
Hall	C₇²×C₉×C₁₉ ⋊ C₂²
Hall	C₇²×C₁₉ ⋊ C₂×D₉
Hall	C₉×C₁₉ ⋊ C₂×C₇⋊D₇
Sylow	C₇² ⋊ C₂×D₉×C₁₉
Sylow	C₉ ⋊ C₂×C₁₉×C₇⋊D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₇⋊D₆₃
commutator, cosocle, hypocenter	C₇²×C₉	C₂²×C₁₉
Frattini	C₃	C₂×C₁₉×C₃⋊(C₇⋊D₇)
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle	C₂×C₃×C₇²×C₁₉	D₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₂×C₁₉

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 16758

A minimal faithful permutation representation — 3 generators on 44 points:

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

Conjugacy classes & character table

8436 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 506);

C2×C19×C7⋊D63 #45691708