C₂×C₆₇×D₄₉ #27190068

order	13132
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₆₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₆₇×D₄₉
unambiguous semidirect product	C₄₉⋊(C₂²×C₆₇)
unambiguous semidirect product	(C₂×C₄₉)⋊(C₂×C₆₇)

Splittings

Fitting	C₂×C₄₉×C₆₇ ⋊ C₂
derived, Sylow	C₄₉ ⋊ C₂²×C₆₇
Hall	C₄₉×C₆₇ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₆₇	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂²×C₆₇
Frattini	C₇	C₂×D₇×C₆₇
Fitting	C₂×C₄₉×C₆₇	C₂
socle	C₂×C₇×C₆₇	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₆₇

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 118
transitive degree	μ_t(G) = 6566

A minimal faithful permutation representation — 2 generators on 118 points:

(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,20)(12,23)(14,25)(17,29)(18,28)(19,27)(21,32)(22,34)(24,36)(26,38)(30,39)(31,40)(33,42)(35,44)(37,46)(41,47)(43,48)(45,49)(50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116);(1,6,24,45,44,23,4,3,14,37,48,34,10,9,8,26,47,42,20,19,18,17,39,40,32,21,31,30,29,28,27,11,33,41,38,16,15,5,22,43,46,25,7,2,12,35,49,36,13)(117,118)

Conjugacy classes & character table

3484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13132, 8);

C2×C67×D49 #27190068