C₇×C₄₇⋊D₄₇ #44525725

order	30926
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₄₇

Aliases

direct product	C₇×C₄₇⋊D₄₇
unambiguous semidirect product	C₄₇⋊(C₇×D₄₇)

Splittings

Fitting, socle, Hall	C₇×C₄₇² ⋊ C₂
derived, Sylow	C₄₇² ⋊ C₂×C₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇	C₄₇⋊D₄₇
commutator, cosocle, hypocenter	C₄₇²	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₄₇²	C₂
LCS	G ▷ C₄₇²
UCS	C₁ ◁ C₇

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 15463

A minimal faithful permutation representation — 3 generators on 101 points:

(1,2,3,4,5,6,7)(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)(51,52)(53,54)(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)(94,95)(96,97)(98,99)(100,101);(55,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57);(8,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10)

Conjugacy classes & character table

7742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30926, 7);

C7×C47⋊D47 #44525725