C₂×C₁₇×C₇⋊D₆₃ #44472624

order	29988
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₁₇×C₇⋊D₆₃
unambiguous semidirect product	(C₂×C₇)⋊(C₁₇×D₆₃)
unambiguous semidirect product	(C₂×C₉)⋊(C₁₇×C₇⋊D₇)

Splittings

Fitting	C₂×C₇²×C₉×C₁₇ ⋊ C₂
derived, Hall	C₇²×C₉ ⋊ C₂²×C₁₇
Hall	C₇²×C₉×C₁₇ ⋊ C₂²
Hall	C₇²×C₁₇ ⋊ C₂×D₉
Hall	C₉×C₁₇ ⋊ C₂×C₇⋊D₇
Sylow	C₇² ⋊ C₂×C₁₇×D₉
Sylow	C₉ ⋊ C₂×C₁₇×C₇⋊D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₇⋊D₆₃
commutator, cosocle, hypocenter	C₇²×C₉	C₂²×C₁₇
Frattini	C₃	C₂×C₁₇×C₃⋊(C₇⋊D₇)
Fitting	C₂×C₇²×C₉×C₁₇	C₂
socle	C₂×C₃×C₇²×C₁₇	D₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₂×C₁₇

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 14994

A minimal faithful permutation representation — 3 generators on 42 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);(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

7548 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 265);

C2×C17×C7⋊D63 #44472624