C₄₉×Dic₂₃ #17985188

order	4508
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₉×Dic₂₃
unambiguous semidirect product	C₂₃⋊(C₄×C₄₉)

Splittings

derived, Sylow	C₂₃ ⋊ C₄×C₄₉
Hall	C₂₃×C₄₉ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₉	D₂₃
commutator, hypocenter	C₂₃	C₄×C₄₉
Frattini	C₂×C₇	C₇×D₂₃
Fitting	C₂×C₂₃×C₄₉	C₂
socle, prime radical, cosocle	C₂×C₇×C₂₃	C₂×C₇
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₄₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 76
transitive degree	μ_t(G) = 4508

A minimal faithful permutation representation — 2 generators on 76 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49)(50,51)(52,53)(54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76);(50,52,51,53)(55,76)(56,75)(57,74)(58,73)(59,72)(60,71)(61,70)(62,69)(63,68)(64,67)(65,66)

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₂₃×C₄₉⋊C₃, C₃×C₄₉×Dic₂₃, C₄₉×Dic₆₉, …
maximal normal subgroup of	Dic₂₃×C₄₉⋊C₃, C₃×C₄₉×Dic₂₃, C₅×C₄₉×Dic₂₃
maximal quotient of	C₃×C₄₉×Dic₂₃, C₄₉×Dic₆₉, C₅×C₄₉×Dic₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4508, 3);

C49×Dic23 #17985188