C₆₇×Dic₄₉ #27190062

order	13132
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×Dic₄₉
unambiguous semidirect product	C₄₉⋊(C₄×C₆₇)

Splittings

derived, Sylow	C₄₉ ⋊ C₄×C₆₇
Hall	C₄₉×C₆₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₆₇	D₄₉
commutator, hypocenter	C₄₉	C₄×C₆₇
Frattini	C₂×C₇	D₇×C₆₇
Fitting	C₂×C₄₉×C₆₇	C₂
socle, prime radical	C₂×C₇×C₆₇	D₇
cosocle	C₂×C₄₉	C₂×C₆₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₆₇

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 120
transitive degree	μ_t(G) = 13132

A minimal faithful permutation representation — 2 generators on 120 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)(21,22)(24,34)(26,36)(30,37)(31,39)(32,38)(33,42)(35,44)(40,45)(41,46)(43,48)(47,49)(50,53,52,51)(54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120);(1,15,39,49,41,19,4,7,28,45,43,32,10,13,16,37,35,33,20,23,25,29,26,24,22,21,34,36,17,14,12,11,42,44,30,8,6,5,38,48,40,18,3,2,27,46,47,31,9)

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, 2);

C67×Dic49 #27190062