C₃×C₂²⋊D₄₉ #11924113

order	1176
isoclinism	isoclinic class of Dic₉₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×C₂²⋊D₄₉

Splittings

Fitting	C₂²×C₃×C₄₉ ⋊ C₂
Hall	C₃×C₄₉ ⋊ D₄
Sylow	C₄₉ ⋊ C₃×D₄

Subgroups

	subgroup	G/H
center	C₂×C₃	C₂×D₄₉
commutator, cosocle	C₂×C₄₉	C₂²×C₃
Frattini	C₂×C₇	C₂×C₃×D₇
Fitting	C₂²×C₃×C₄₉	C₂
socle	C₂×C₃×C₇	C₂×D₇
hypercenter	C₂²×C₃	D₄₉
hypocenter	C₄₉	C₃×D₄
LCS	G ▷ C₂×C₄₉ ▷ C₄₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 56
transitive degree	μ_t(G) = 588

A minimal faithful permutation representation — 2 generators on 56 points:

(1,2,3)(4,31,38,25,45,43,12,10,40,27,14,51,34,7,19,29,15,41,50,22,16,32,17,8,49,44,13,28,20,9,30,52,35,26,39,11,5,42,46,23,37,33,6,18,48,36,24,47,21)(54,56);(5,7)(6,10)(8,13)(9,16)(11,19)(12,18)(14,23)(15,26)(17,28)(20,32)(21,31)(22,30)(24,25)(27,37)(29,39)(33,40)(34,42)(35,41)(36,45)(38,47)(43,48)(44,49)(46,51)(50,52)(53,54)(55,56)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 28);

C3×C22⋊D49 #11924113