C₄₉×Dic₆₇ #27190063

order	13132
isoclinism	isoclinic class of D₆₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₉×Dic₆₇
unambiguous semidirect product	C₆₇⋊(C₄×C₄₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₉	D₆₇
commutator, hypocenter	C₆₇	C₄×C₄₉
Frattini	C₂×C₇	C₇×D₆₇
Fitting	C₂×C₄₉×C₆₇	C₂
socle, prime radical, cosocle	C₂×C₇×C₆₇	C₂×C₇
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₄₉

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:

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

Conjugacy classes & character table

3430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13132, 3);

C49×Dic67 #27190063