C₂×C₅×C₄₃⋊D₄₃ #49149758

order	36980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂×C₄₃

Aliases

direct product	C₂×C₅×C₄₃⋊D₄₃
unambiguous semidirect product	(C₂×C₄₃)⋊(C₅×D₄₃)

Splittings

Fitting, socle	C₂×C₅×C₄₃² ⋊ C₂
derived, Sylow	C₄₃² ⋊ C₂²×C₅
Hall	C₅×C₄₃² ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	C₄₃⋊D₄₃
commutator, cosocle, hypocenter	C₄₃²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₄₃²	C₂
LCS	G ▷ C₄₃²
UCS	C₁ ◁ C₂×C₅

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 18490

A minimal faithful permutation representation — 3 generators on 93 points:

(3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93);(1,2)(51,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53);(8,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10)

Conjugacy classes & character table

9260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36980, 31);

C2×C5×C43⋊D43 #49149758